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x=1+2+4+8+16+...
2x=2+4+8+16+...
2x-x=(2+4+8+16+...)-(1+2+4+8+16+...)
x=-1
But x is clearly infinity, so infinity equals -1. Where's the error with this? -- 76.77.139.243 ( talk) 13:26, 14 June 2010 (UTC)
One error is that you can't subtract series in that way unless they converge to a finite number.
Infinity minus infinity is an indeterminate form. That means that if ƒ(x) and g(x) can both be made as large as desired by making x close enough to some specified point (which may be infinite) then ƒ(x) − g(x) may approach anything, depending on which functions ƒ and g are. Michael Hardy ( talk) 13:45, 14 June 2010 (UTC)
There is only one error here. The expression is not a sum. It is shorthand for a limit. Treating it as a sum and attributing some of the standard properties of sums (like distributivity, commutativity and/or associativity) creates the trouble. DVdm ( talk) 14:33, 14 June 2010 (UTC)
Hi everyone. I'm looking for a program to draw graphs easily (I do mean graphs not charts - essentially circles connected by lines). I'd like a program which has the following:
Does anyone know any software which can do this? - mattbuck ( Talk) 17:53, 14 June 2010 (UTC)
How do you write limits of integration after finding what the integral is. For example, let's say if the question was to integrate x^2 from 0 to 1, the (partial) solution to this is x^2/2 evaluated from 0 to 1, how would you write this in TeX? 142.244.151.247 ( talk) 21:07, 14 June 2010 (UTC)
The standard is square brackets on either side:
I only mentioned the one-sided brackets so the person setting the question could use the functionality in other settings. The single line on the right is usually used as a short hand for evaluation. So ⅓x3 evaluated at x = 0 can be written as
Mathematics desk | ||
---|---|---|
< June 13 | << May | June | Jul >> | June 15 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
x=1+2+4+8+16+...
2x=2+4+8+16+...
2x-x=(2+4+8+16+...)-(1+2+4+8+16+...)
x=-1
But x is clearly infinity, so infinity equals -1. Where's the error with this? -- 76.77.139.243 ( talk) 13:26, 14 June 2010 (UTC)
One error is that you can't subtract series in that way unless they converge to a finite number.
Infinity minus infinity is an indeterminate form. That means that if ƒ(x) and g(x) can both be made as large as desired by making x close enough to some specified point (which may be infinite) then ƒ(x) − g(x) may approach anything, depending on which functions ƒ and g are. Michael Hardy ( talk) 13:45, 14 June 2010 (UTC)
There is only one error here. The expression is not a sum. It is shorthand for a limit. Treating it as a sum and attributing some of the standard properties of sums (like distributivity, commutativity and/or associativity) creates the trouble. DVdm ( talk) 14:33, 14 June 2010 (UTC)
Hi everyone. I'm looking for a program to draw graphs easily (I do mean graphs not charts - essentially circles connected by lines). I'd like a program which has the following:
Does anyone know any software which can do this? - mattbuck ( Talk) 17:53, 14 June 2010 (UTC)
How do you write limits of integration after finding what the integral is. For example, let's say if the question was to integrate x^2 from 0 to 1, the (partial) solution to this is x^2/2 evaluated from 0 to 1, how would you write this in TeX? 142.244.151.247 ( talk) 21:07, 14 June 2010 (UTC)
The standard is square brackets on either side:
I only mentioned the one-sided brackets so the person setting the question could use the functionality in other settings. The single line on the right is usually used as a short hand for evaluation. So ⅓x3 evaluated at x = 0 can be written as