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Isn't 0 over 0 is a determinate form because if you keep multiplying very small number very few times you just get 0. -- Taku 02:25, Nov 15, 2003 (UTC)
0/0 is indeterminate since if it had some definite value, say x, so 0x=0. But any number satisfies that equation for x, so 0/0 has no definite or determinable value. Dysprosia 02:28, 15 Nov 2003 (UTC)
In the sense of this article, 0/0 is indeterminate because if f(x) and g(x) both approach 0 as x approaches something, then f(x)/g(x) can approach a number that depends on which functions f and g are. (That does not detract from the elegance of Dysprosia's observation, however.) Michael Hardy 20:18, 15 Nov 2003 (UTC)
I've just moved some material from zero divided by zero to this page performing significant changes to it to make it apropriate for this page. I am planning to move more material in a few days time but not necessarily to this page and maybe to a subpage of this page. Barnaby dawson 19:56, 20 Sep 2004 (UTC)
After an edit clash, I've added to the second paragraph. Charles Matthews 11:05, 18 Mar 2005 (UTC)
I've now done further work on that discussion. Charles Matthews 11:16, 18 Mar 2005 (UTC)
The form oo^oo is missing from the list.
It can be indeterminate in a weak sense, like 1/0 (but perhaps a bit stronger). For example, as x approaches 0 from the right, (1/x)1/x approaches infinity (from the left), while (1/x)-1/x approaches zero (from the right). But nothing of this form can converge to any non-zero finite value (because the logarithm must converge to infinity). I'm not sure if this should count as indeterminate or not; the precise definition that I've just written says that it is, but one could easily fix that so that it's not. -- Toby Bartels 01:57, 23 May 2006 (UTC)
User:Michael Hardy, at 15:37, 18 December 2005, wrote in this diff:
(copied here for future reference by Oleg Alexandrov ( talk) 00:16, 19 December 2005 (UTC))
The "Discussion" section had a problem paragraph (reading "By contrast "1/0" is not an indeterminate form because there is no range of different values that f/g could if f approaches 1 and g approaches 0."). There was at least a missing word (between could and if). I attempted to correct that and add more detail to clarify it, but then realized I still don't understand the distinction which is the whole point of the article.
Several times 1/0 is contrasted with 0/0, but the only characterization of this contrast is that there is "no range of different values" without elaboration. But f/g could have a limit of either +∞ or -∞ depending on whether the function g approaches 0 from the + or - side. So there seems to be more than one "value" possible among limits approaching 1/0. Just how is this determinate while 0/0 is not? Whatever the answer, I think the article needs improvement in explaining this. - R. S. Shaw 00:58, 13 March 2006 (UTC)
I think that the whole article is rather unclear in a few ways, first of all that this is fudnamentally about limits (although of course, that is not your problem, R. S. Shaw). With this in mind, I'm going to rewrite it a good deal right now, and I should be able to address your (Shaw's) problem at the same time. -- Toby Bartels 20:29, 22 May 2006 (UTC)
The lead sentence says
This is clearly wrong - an indeterminate form may be obtained by substituting limits of subexpressions, but the form itself is just a few symbols and doesn't have a "limit", it has a "value" (or more precisely, it does not have a value). That is, the question "What is the limit of 0/0?" is meaningless. CMummert 02:22, 29 December 2006 (UTC)
I think the situation is being looked into the wrong way. Say you had (x^2-9)/(x+3). Someone that didn't know that x+3 is a conjugate of x^2-9 would tell you that -3 gives an undefined answer. Yet someone who factored would get x-3, and say that all values are defined. I take this to mean that in a situation like x^2/x, 0/0 is 0. However, in the cases where it's 0(a)/0, where a is any number except 0, the result is a as 0/0 would negate eachother and equal one. An example is above. And don't gimme a "but my calculator says no." k, I want to know what you guys think. Also, another example is x/x, every number outside of zero gives a 1 answer, so it would be expected that 0/0 gives a one answer. This even works with x^2/x. The reason (0,0) is a point, and not (0,1), is because when you expand ((0)^2)/0 you get 0*0/0. 0/0 is one, and that leaves 0*1, which gives 0. —Preceding unsigned comment added by 66.66.92.167 ( talk) 07:11, 3 January 2007
I've changed "The indeterminate forms include [...]" to "The indeterminate forms are [...]" on the assumption that the list is exhaustive. Previous wording admitted interpretation of list as a subset.
If the given list is not exhaustive, I believe the best compromise is "The indeterminate forms (as described this article) are [...]". That is to say, whether or not the list is exhaustive, the current wording is needlessly ambiguous. 23:29, 7 March 2007 (UTC)
A separate critique is that it seems better to say "are expressed by/using/as" or "are referred to by/as" in place of "are". It may be confusing to many readers to say such-and-such is 0/0 as it might seem to imply (as we almost always intend when writing such expressions) that 0/0 represents a number rather than a form. I have not made this change; I don't know what wording best resolves this potential misreading. Please discuss here. 23:35, 7 March 2007 (UTC)
Example: Define f as f(x)=(x+3)(x-3)/(x-3) for x other than 3, and f(x)=6 for x=3. This function is continuous at x=3, even though its limit as x goes to 3 is of the indeterminate form 0/0. FilipeS 18:06, 11 June 2007 (UTC)
What is your source for claiming that being an indeterminate form has anything to do with the arity of the operations involved? I've never heard of such a notion! Exponentiation is a unary operation, yet 1 to the power of infinity is still an indetermination. FilipeS 13:53, 12 June 2007 (UTC)
It depends on how you define it: the exponential function is unary. And you can regard division as binary, f(x, y) = x/y, or unary, g(x) = x/b, or h(x) = a/x. Which is why bringing arity into the conversation makes no sense to me. Indeterminate forms have to do with calculus and limits, not algebra and arity. FilipeS
(This goes back to Carl's remark that "It's more a question of how closely you want the sources to match the phrasing of the article.") I don't think that's the whole issue. While no doubt someone has done it, I don't believe it has ever been standard to give a general, abstract definition of "indeterminate form". If you want to discuss discontinuous funcions, you talk about discontinuous functions; the "indeterminate form" terminology is a fifth wheel when you get to that level of abstraction.
Historically the phrase has been used to give calculus students a way of detecting situations where they have to apply extra care when computing a limit, without bringing up anything as sophisticated as the definition of a continuous function from R2 to R. It's an enumerated collection of situations; no rule is given for extending it. I think that should be the focus of this article. Something like, say, ei∞ could easily be added to the list, but historically, it has not been.
If generalizations can be sourced, they can be added, but they should be clearly marked as generalizations of the notion, not part of the standard interpretation of "indeterminate form". -- Trovatore 20:13, 12 June 2007 (UTC)
I would like to clarify the article, but apparently I'm not succeeding. I agree there are only seven indeterminate forms. If the purpose of that paragraph was only to generalize them, it should be removed. But I think it can be salvaged, and has merit, as an explanation of why these particular seven expressions are indeterminate but the rest aren't. The point is that they are the only expressions involving one of the operations of addition, subtraction, multiplication, division, and exponentiation and two values from the extended real numbers such that the value of the operation on those two values is not determined by continuity, and therefore it isn't possible to commute the limit across the operation. That point ought to be conveyed by the article, but if the current paragraph isn't doing it, I'll be glad to rewrite it from scratch. — Carl ( CBM · talk) 23:44, 12 June 2007 (UTC)
I'm confident that the four people in this discussion all understand perfectly what's going on with indeterminate forms. The question is: if someone in 11th grade asked you for a one-sentence explanation of why these seven forms are called indeterminate but the others are not, what would you say? — Carl ( CBM · talk) 18:58, 19 June 2007 (UTC)
in the 0^0 form it sayed that if f & g both analytic and g in not fixed zero in the nighberhood of the limit than f(x)^g(x) is always 1 in that limit which is just false it is often the case but consider the example: f(x)=3^x which is positive for all x & g(x)=1/x both zeroing at negative infinity but f(x)^g(x) is clearly 3 whats up with that ?
I didn't see any mention of negative infinity in the article. I only mention this because my Calculus book (Calculus - Early Transcendentals 6th Edition by James Stewart) says that -∞/-∞ is also indeterminate. Also, what about the forms of -∞/∞ and ∞/-∞? Are they all indeterminate forms? Thanks. BuddhaBubba ( talk) 00:03, 20 July 2010 (UTC)
Would Tan(90 degrees) be an indeterminate form. The tan wave goes to infinity at 90. Also if you imagine a right angled triangle and imagine the adjacent side getting smaller and smaller theta gets closer and closer to 90 making tan(theta) closer and closer to tan(90) and therefore undefined. To have a right angled triangle with Tan(90) it's adjacent side would have a length of zero and the hypotenuse and opposite sides would be the same length. 90 would be theta, the angle between the adjacent and opposite sides would be 90 and the third angle would be 0. In effect it would be a straight line. However basic trigonometry still works.
For example, if the hypotenuse and opposite had both got a length of 1 then;
Sin(90)=1/1 which is correct. Cos(90)=0/1 which is correct. Sin(0)=0/1 which is correct. Cos(0)=1/1 which is correct. Tan(0)=0/1 which is correct.
However, Tan(90)=1/0. Which is an indeterminate form. This means that Tan(90) can be converted to 1/0 (and other determinate forms using l'hopitals rule).
If we were trying to work out the length of the hypotenuse and opposite it wouldn't work because we'd get Tan(90)=Hypotenuse/0. This happens because the hypotenuse and opposite could be any length as long as they are the same, the angles would be unchanged.
As well as this Tan(theta)=sin(theta)/cos(theta) so Tan(90)=Sin(90)/Cos(90). Sin(90) is 1 and Cos(90) is 0. Therefore Tan(90) again equals 1/0.
So is Tan(90) an indeterminate form? It tends towards infinity on the Tan graph. The limit of Tan theta as theta approaches 90 is ±∞. Also are all of the above valid arguments? — Preceding unsigned comment added by 86.140.32.172 ( talk) 14:40, 20 July 2012 (UTC)
These don't seem to be indeterminate based ont he way the article explains the term.
1^∞
A power is the number times itself that many times. 1 times itself a unlimited number of times would be 1.
0 × ∞
Standard rule is any number times zero is zero ie 0 x X = 0 so it doesn't matter what X is.
If these are indeterminate the article should explain why they are. 216.31.124.44 ( talk) 05:31, 18 January 2013 (UTC)
Some sources say that 0/0 is an indeterminate form, but not all. For instance, in "Mathematical Analysis I, Volume 1 By Claudio Canuto, Anita Tabacco", when f(x),g(x) converge to 0, the expression f(x)/g(x) is an indeterminate form when x -> 0, while 0/0 denotes an indeterminate form.
In the subsection "Evaluating indeterminate forms", the word "indeterminate form" refers to f(x)/g(x) (with x -> 0), just like in the definition in the above mentioned book.
In many books, the indeterminate forms are frequently simply listed, without giving any definition. If the main page gives a definition, it should probably cite something for its definition. Moreover, when writing the definition, keep in mind that in some definitions, floor(0) is an indeterminate form, whereas in other definitions, it is not (I have no preference between those options; this is not a form that a calculus student is likely to encounter. But it would be good if the definition is clarified one way or the other). MvH ( talk) 16:06, 12 February 2014 (UTC)MvH
The article claims
This strikes me as patently false: it depends on the "operation" of exponentiation that is ill-defined on the complex numbers and cannot be defined as a continuous function in a punctured neighbourhood of (0,0). Any sensible interpretation will rely on the multivalued complex logarithm, which yields no limit even if one allows limits of multifunctions. Reliance on a single-valued definition requires a "sensible" branch of the exponentiation to be taken, as it seems to me that spiral branches exist that yield any limit that one chooses. A complex function f(z)g(z) in a bland statement like this without defining the exponentiation or mentioning the mathematically esoteric aspects seems out of place here. I notice that this has survived edits by not-so-clueless editors, so perhaps someone could explain why this claim should remain in the article, or where I've gone wrong? — Quondum 17:04, 22 February 2014 (UTC)
Not sure where to place this.
http://dubai-computer-services.com/articles/infinities_by_khawar_nehal_19_mar_2014-1.pdf
If you can guide me as to where this can go, then I can place it there.
Regards,
Khawar Nehal — Preceding unsigned comment added by 94.203.214.192 ( talk) 10:03, 23 March 2014 (UTC)
This article section used to read:
Now it reads:
The changes made were not for the better. A simple and correct sentence was changed into one that is more convoluted, more obscure, and actually somewhat less accurate: algebraic expressions such as 0+∞ or 02 or 01/2 do not have "limiting forms"; functions do. At most, one might say that 0+∞ is a limiting form. And everyone agrees that 0+∞ can be defined as zero, so there's no mathematical sin in plainly writing "0+∞=0". FilipeS ( talk) 16:27, 6 August 2014 (UTC)
The expression "indeterminate form" is as unanalyzable as the derivative dy/dx in the standard approach. Namely, an indeterminate form is NOT a form that's indeterminate rather than being determinate. Therefore the page should avoid using the term "form", as in the phrase "such-and-such a form is not indeterminate". Tkuvho ( talk) 09:10, 17 December 2014 (UTC)
The unique reference provided here is to an obscure article in an obscure journal by Louis M. Rotando and Henry Korn (January 1977). Is this really the ultimate reference on indeterminate forms? Tkuvho ( talk) 09:50, 11 January 2015 (UTC)
Now that I've linked Algebraic operation, I notice that three of the listed indeterminate forms (namely those that involve exponentiation) relate to a function that is not an algebraic operation as defined by that article. It think that it is reasonable to deduce that the definition is flawed, since the cases of exponentiation are clearly historically notable examples. — Quondum 23:46, 19 April 2015 (UTC)
0/0 is indeterminate, russian word equivalent sense will be "неоднозначно".
10/0 is undefined, russian word equivalent sense will be "неопределено".
188.208.126.82 (
talk)
14:11, 9 June 2023 (UTC)
Wolfram alpha uses this list of indeterminate forms,
should we add the missing ones to the list on the page? 2007GabrielT ( talk) 12:59, 13 November 2023 (UTC)
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Isn't 0 over 0 is a determinate form because if you keep multiplying very small number very few times you just get 0. -- Taku 02:25, Nov 15, 2003 (UTC)
0/0 is indeterminate since if it had some definite value, say x, so 0x=0. But any number satisfies that equation for x, so 0/0 has no definite or determinable value. Dysprosia 02:28, 15 Nov 2003 (UTC)
In the sense of this article, 0/0 is indeterminate because if f(x) and g(x) both approach 0 as x approaches something, then f(x)/g(x) can approach a number that depends on which functions f and g are. (That does not detract from the elegance of Dysprosia's observation, however.) Michael Hardy 20:18, 15 Nov 2003 (UTC)
I've just moved some material from zero divided by zero to this page performing significant changes to it to make it apropriate for this page. I am planning to move more material in a few days time but not necessarily to this page and maybe to a subpage of this page. Barnaby dawson 19:56, 20 Sep 2004 (UTC)
After an edit clash, I've added to the second paragraph. Charles Matthews 11:05, 18 Mar 2005 (UTC)
I've now done further work on that discussion. Charles Matthews 11:16, 18 Mar 2005 (UTC)
The form oo^oo is missing from the list.
It can be indeterminate in a weak sense, like 1/0 (but perhaps a bit stronger). For example, as x approaches 0 from the right, (1/x)1/x approaches infinity (from the left), while (1/x)-1/x approaches zero (from the right). But nothing of this form can converge to any non-zero finite value (because the logarithm must converge to infinity). I'm not sure if this should count as indeterminate or not; the precise definition that I've just written says that it is, but one could easily fix that so that it's not. -- Toby Bartels 01:57, 23 May 2006 (UTC)
User:Michael Hardy, at 15:37, 18 December 2005, wrote in this diff:
(copied here for future reference by Oleg Alexandrov ( talk) 00:16, 19 December 2005 (UTC))
The "Discussion" section had a problem paragraph (reading "By contrast "1/0" is not an indeterminate form because there is no range of different values that f/g could if f approaches 1 and g approaches 0."). There was at least a missing word (between could and if). I attempted to correct that and add more detail to clarify it, but then realized I still don't understand the distinction which is the whole point of the article.
Several times 1/0 is contrasted with 0/0, but the only characterization of this contrast is that there is "no range of different values" without elaboration. But f/g could have a limit of either +∞ or -∞ depending on whether the function g approaches 0 from the + or - side. So there seems to be more than one "value" possible among limits approaching 1/0. Just how is this determinate while 0/0 is not? Whatever the answer, I think the article needs improvement in explaining this. - R. S. Shaw 00:58, 13 March 2006 (UTC)
I think that the whole article is rather unclear in a few ways, first of all that this is fudnamentally about limits (although of course, that is not your problem, R. S. Shaw). With this in mind, I'm going to rewrite it a good deal right now, and I should be able to address your (Shaw's) problem at the same time. -- Toby Bartels 20:29, 22 May 2006 (UTC)
The lead sentence says
This is clearly wrong - an indeterminate form may be obtained by substituting limits of subexpressions, but the form itself is just a few symbols and doesn't have a "limit", it has a "value" (or more precisely, it does not have a value). That is, the question "What is the limit of 0/0?" is meaningless. CMummert 02:22, 29 December 2006 (UTC)
I think the situation is being looked into the wrong way. Say you had (x^2-9)/(x+3). Someone that didn't know that x+3 is a conjugate of x^2-9 would tell you that -3 gives an undefined answer. Yet someone who factored would get x-3, and say that all values are defined. I take this to mean that in a situation like x^2/x, 0/0 is 0. However, in the cases where it's 0(a)/0, where a is any number except 0, the result is a as 0/0 would negate eachother and equal one. An example is above. And don't gimme a "but my calculator says no." k, I want to know what you guys think. Also, another example is x/x, every number outside of zero gives a 1 answer, so it would be expected that 0/0 gives a one answer. This even works with x^2/x. The reason (0,0) is a point, and not (0,1), is because when you expand ((0)^2)/0 you get 0*0/0. 0/0 is one, and that leaves 0*1, which gives 0. —Preceding unsigned comment added by 66.66.92.167 ( talk) 07:11, 3 January 2007
I've changed "The indeterminate forms include [...]" to "The indeterminate forms are [...]" on the assumption that the list is exhaustive. Previous wording admitted interpretation of list as a subset.
If the given list is not exhaustive, I believe the best compromise is "The indeterminate forms (as described this article) are [...]". That is to say, whether or not the list is exhaustive, the current wording is needlessly ambiguous. 23:29, 7 March 2007 (UTC)
A separate critique is that it seems better to say "are expressed by/using/as" or "are referred to by/as" in place of "are". It may be confusing to many readers to say such-and-such is 0/0 as it might seem to imply (as we almost always intend when writing such expressions) that 0/0 represents a number rather than a form. I have not made this change; I don't know what wording best resolves this potential misreading. Please discuss here. 23:35, 7 March 2007 (UTC)
Example: Define f as f(x)=(x+3)(x-3)/(x-3) for x other than 3, and f(x)=6 for x=3. This function is continuous at x=3, even though its limit as x goes to 3 is of the indeterminate form 0/0. FilipeS 18:06, 11 June 2007 (UTC)
What is your source for claiming that being an indeterminate form has anything to do with the arity of the operations involved? I've never heard of such a notion! Exponentiation is a unary operation, yet 1 to the power of infinity is still an indetermination. FilipeS 13:53, 12 June 2007 (UTC)
It depends on how you define it: the exponential function is unary. And you can regard division as binary, f(x, y) = x/y, or unary, g(x) = x/b, or h(x) = a/x. Which is why bringing arity into the conversation makes no sense to me. Indeterminate forms have to do with calculus and limits, not algebra and arity. FilipeS
(This goes back to Carl's remark that "It's more a question of how closely you want the sources to match the phrasing of the article.") I don't think that's the whole issue. While no doubt someone has done it, I don't believe it has ever been standard to give a general, abstract definition of "indeterminate form". If you want to discuss discontinuous funcions, you talk about discontinuous functions; the "indeterminate form" terminology is a fifth wheel when you get to that level of abstraction.
Historically the phrase has been used to give calculus students a way of detecting situations where they have to apply extra care when computing a limit, without bringing up anything as sophisticated as the definition of a continuous function from R2 to R. It's an enumerated collection of situations; no rule is given for extending it. I think that should be the focus of this article. Something like, say, ei∞ could easily be added to the list, but historically, it has not been.
If generalizations can be sourced, they can be added, but they should be clearly marked as generalizations of the notion, not part of the standard interpretation of "indeterminate form". -- Trovatore 20:13, 12 June 2007 (UTC)
I would like to clarify the article, but apparently I'm not succeeding. I agree there are only seven indeterminate forms. If the purpose of that paragraph was only to generalize them, it should be removed. But I think it can be salvaged, and has merit, as an explanation of why these particular seven expressions are indeterminate but the rest aren't. The point is that they are the only expressions involving one of the operations of addition, subtraction, multiplication, division, and exponentiation and two values from the extended real numbers such that the value of the operation on those two values is not determined by continuity, and therefore it isn't possible to commute the limit across the operation. That point ought to be conveyed by the article, but if the current paragraph isn't doing it, I'll be glad to rewrite it from scratch. — Carl ( CBM · talk) 23:44, 12 June 2007 (UTC)
I'm confident that the four people in this discussion all understand perfectly what's going on with indeterminate forms. The question is: if someone in 11th grade asked you for a one-sentence explanation of why these seven forms are called indeterminate but the others are not, what would you say? — Carl ( CBM · talk) 18:58, 19 June 2007 (UTC)
in the 0^0 form it sayed that if f & g both analytic and g in not fixed zero in the nighberhood of the limit than f(x)^g(x) is always 1 in that limit which is just false it is often the case but consider the example: f(x)=3^x which is positive for all x & g(x)=1/x both zeroing at negative infinity but f(x)^g(x) is clearly 3 whats up with that ?
I didn't see any mention of negative infinity in the article. I only mention this because my Calculus book (Calculus - Early Transcendentals 6th Edition by James Stewart) says that -∞/-∞ is also indeterminate. Also, what about the forms of -∞/∞ and ∞/-∞? Are they all indeterminate forms? Thanks. BuddhaBubba ( talk) 00:03, 20 July 2010 (UTC)
Would Tan(90 degrees) be an indeterminate form. The tan wave goes to infinity at 90. Also if you imagine a right angled triangle and imagine the adjacent side getting smaller and smaller theta gets closer and closer to 90 making tan(theta) closer and closer to tan(90) and therefore undefined. To have a right angled triangle with Tan(90) it's adjacent side would have a length of zero and the hypotenuse and opposite sides would be the same length. 90 would be theta, the angle between the adjacent and opposite sides would be 90 and the third angle would be 0. In effect it would be a straight line. However basic trigonometry still works.
For example, if the hypotenuse and opposite had both got a length of 1 then;
Sin(90)=1/1 which is correct. Cos(90)=0/1 which is correct. Sin(0)=0/1 which is correct. Cos(0)=1/1 which is correct. Tan(0)=0/1 which is correct.
However, Tan(90)=1/0. Which is an indeterminate form. This means that Tan(90) can be converted to 1/0 (and other determinate forms using l'hopitals rule).
If we were trying to work out the length of the hypotenuse and opposite it wouldn't work because we'd get Tan(90)=Hypotenuse/0. This happens because the hypotenuse and opposite could be any length as long as they are the same, the angles would be unchanged.
As well as this Tan(theta)=sin(theta)/cos(theta) so Tan(90)=Sin(90)/Cos(90). Sin(90) is 1 and Cos(90) is 0. Therefore Tan(90) again equals 1/0.
So is Tan(90) an indeterminate form? It tends towards infinity on the Tan graph. The limit of Tan theta as theta approaches 90 is ±∞. Also are all of the above valid arguments? — Preceding unsigned comment added by 86.140.32.172 ( talk) 14:40, 20 July 2012 (UTC)
These don't seem to be indeterminate based ont he way the article explains the term.
1^∞
A power is the number times itself that many times. 1 times itself a unlimited number of times would be 1.
0 × ∞
Standard rule is any number times zero is zero ie 0 x X = 0 so it doesn't matter what X is.
If these are indeterminate the article should explain why they are. 216.31.124.44 ( talk) 05:31, 18 January 2013 (UTC)
Some sources say that 0/0 is an indeterminate form, but not all. For instance, in "Mathematical Analysis I, Volume 1 By Claudio Canuto, Anita Tabacco", when f(x),g(x) converge to 0, the expression f(x)/g(x) is an indeterminate form when x -> 0, while 0/0 denotes an indeterminate form.
In the subsection "Evaluating indeterminate forms", the word "indeterminate form" refers to f(x)/g(x) (with x -> 0), just like in the definition in the above mentioned book.
In many books, the indeterminate forms are frequently simply listed, without giving any definition. If the main page gives a definition, it should probably cite something for its definition. Moreover, when writing the definition, keep in mind that in some definitions, floor(0) is an indeterminate form, whereas in other definitions, it is not (I have no preference between those options; this is not a form that a calculus student is likely to encounter. But it would be good if the definition is clarified one way or the other). MvH ( talk) 16:06, 12 February 2014 (UTC)MvH
The article claims
This strikes me as patently false: it depends on the "operation" of exponentiation that is ill-defined on the complex numbers and cannot be defined as a continuous function in a punctured neighbourhood of (0,0). Any sensible interpretation will rely on the multivalued complex logarithm, which yields no limit even if one allows limits of multifunctions. Reliance on a single-valued definition requires a "sensible" branch of the exponentiation to be taken, as it seems to me that spiral branches exist that yield any limit that one chooses. A complex function f(z)g(z) in a bland statement like this without defining the exponentiation or mentioning the mathematically esoteric aspects seems out of place here. I notice that this has survived edits by not-so-clueless editors, so perhaps someone could explain why this claim should remain in the article, or where I've gone wrong? — Quondum 17:04, 22 February 2014 (UTC)
Not sure where to place this.
http://dubai-computer-services.com/articles/infinities_by_khawar_nehal_19_mar_2014-1.pdf
If you can guide me as to where this can go, then I can place it there.
Regards,
Khawar Nehal — Preceding unsigned comment added by 94.203.214.192 ( talk) 10:03, 23 March 2014 (UTC)
This article section used to read:
Now it reads:
The changes made were not for the better. A simple and correct sentence was changed into one that is more convoluted, more obscure, and actually somewhat less accurate: algebraic expressions such as 0+∞ or 02 or 01/2 do not have "limiting forms"; functions do. At most, one might say that 0+∞ is a limiting form. And everyone agrees that 0+∞ can be defined as zero, so there's no mathematical sin in plainly writing "0+∞=0". FilipeS ( talk) 16:27, 6 August 2014 (UTC)
The expression "indeterminate form" is as unanalyzable as the derivative dy/dx in the standard approach. Namely, an indeterminate form is NOT a form that's indeterminate rather than being determinate. Therefore the page should avoid using the term "form", as in the phrase "such-and-such a form is not indeterminate". Tkuvho ( talk) 09:10, 17 December 2014 (UTC)
The unique reference provided here is to an obscure article in an obscure journal by Louis M. Rotando and Henry Korn (January 1977). Is this really the ultimate reference on indeterminate forms? Tkuvho ( talk) 09:50, 11 January 2015 (UTC)
Now that I've linked Algebraic operation, I notice that three of the listed indeterminate forms (namely those that involve exponentiation) relate to a function that is not an algebraic operation as defined by that article. It think that it is reasonable to deduce that the definition is flawed, since the cases of exponentiation are clearly historically notable examples. — Quondum 23:46, 19 April 2015 (UTC)
0/0 is indeterminate, russian word equivalent sense will be "неоднозначно".
10/0 is undefined, russian word equivalent sense will be "неопределено".
188.208.126.82 (
talk)
14:11, 9 June 2023 (UTC)
Wolfram alpha uses this list of indeterminate forms,
should we add the missing ones to the list on the page? 2007GabrielT ( talk) 12:59, 13 November 2023 (UTC)