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4^x+4^1/x=18 — Preceding unsigned comment added by 49.244.51.160 ( talk) 04:23, 16 September 2011 (UTC)
The current image under section Exponentiation#Zero to the zero power shows a 3D plot of z=|x|y, x,y∈ℝ. My impression is that the only purpose of for plotting the absolute value is to give a mirror image for a different perspective. I think that this is potentially confusing and adds very little, though the image is in many respects very good. Would some soul be able to replace this with a similar image showing only x≥0?
Secondly, three of the four green curves through (x,y)=(0,0) have no formula that is evident from inspection of the curves. It might be worthwhile replacing these with curves of constant y/x, where their form is illustrated perhaps by a plane hanging from the respective curve to the plane z=0. This will more clearly illustrate the limit as approached from any fixed direction other than along x=0. — Quondum ☏ ✎ 09:26, 14 February 2012 (UTC)
In the section listing the 'pros' of having 0^0 = 1, the final point given is that it satisfies differentiating x^n, saying 'the power rule is not valid for n = 1 at x = 0 unless 0^0 = 1.' This would mean d/dx (0) = 1, which is definitely not true. — Preceding unsigned comment added by 2.27.26.57 ( talk) 21:48, 14 February 2012 (UTC)
I somehow disfavour writing, in that section, e.g., 3. (2^4)^2 = 2^8 = 256 because it suggests that calculation of (2^4)^2 is done via calculation of 2^8, while the idea is the converse: One calculates the required powers of 2 via squaring of the previous result, thus: 2^8 = (2^4)^2 = 16^2 = 256 — that's the way the reasoning and calculation goes, not the other way round. — MFH: Talk 23:58, 16 May 2012 (UTC)
Negative Exponents redirect here, but I did not find where these are defined, neither here nor at algebraic notation, which dabs me to Mathematical notation. -- Pawyilee ( talk) 04:36, 9 September 2012 (UTC)
Negative exponents are defined in the section Exponentiation#Arbitrary_integer_exponents. Jowa fan ( talk) 06:58, 9 September 2012 (UTC)
The section Positive integer exponents begins:
&c
I suggest the heading be changed to Nonnegative integer exponents and the beginning to:
&c
This is to emphasize that is a possible definition rather than a matter of religious faith. I request your comments. Bo Jacoby ( talk) 08:31, 22 November 2012 (UTC).
Quondum, are you for or against the suggested change? Bo Jacoby ( talk) 21:56, 22 November 2012 (UTC).
I think everything regarding 0^0 is covered perfectly well in that section, and there is no need to rehash the discussions that already led to the current state of the article. — Carl ( CBM · talk) 23:29, 22 November 2012 (UTC)
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 2005 | ← | Archive 2010 | Archive 2011 | Archive 2012 |
4^x+4^1/x=18 — Preceding unsigned comment added by 49.244.51.160 ( talk) 04:23, 16 September 2011 (UTC)
The current image under section Exponentiation#Zero to the zero power shows a 3D plot of z=|x|y, x,y∈ℝ. My impression is that the only purpose of for plotting the absolute value is to give a mirror image for a different perspective. I think that this is potentially confusing and adds very little, though the image is in many respects very good. Would some soul be able to replace this with a similar image showing only x≥0?
Secondly, three of the four green curves through (x,y)=(0,0) have no formula that is evident from inspection of the curves. It might be worthwhile replacing these with curves of constant y/x, where their form is illustrated perhaps by a plane hanging from the respective curve to the plane z=0. This will more clearly illustrate the limit as approached from any fixed direction other than along x=0. — Quondum ☏ ✎ 09:26, 14 February 2012 (UTC)
In the section listing the 'pros' of having 0^0 = 1, the final point given is that it satisfies differentiating x^n, saying 'the power rule is not valid for n = 1 at x = 0 unless 0^0 = 1.' This would mean d/dx (0) = 1, which is definitely not true. — Preceding unsigned comment added by 2.27.26.57 ( talk) 21:48, 14 February 2012 (UTC)
I somehow disfavour writing, in that section, e.g., 3. (2^4)^2 = 2^8 = 256 because it suggests that calculation of (2^4)^2 is done via calculation of 2^8, while the idea is the converse: One calculates the required powers of 2 via squaring of the previous result, thus: 2^8 = (2^4)^2 = 16^2 = 256 — that's the way the reasoning and calculation goes, not the other way round. — MFH: Talk 23:58, 16 May 2012 (UTC)
Negative Exponents redirect here, but I did not find where these are defined, neither here nor at algebraic notation, which dabs me to Mathematical notation. -- Pawyilee ( talk) 04:36, 9 September 2012 (UTC)
Negative exponents are defined in the section Exponentiation#Arbitrary_integer_exponents. Jowa fan ( talk) 06:58, 9 September 2012 (UTC)
The section Positive integer exponents begins:
&c
I suggest the heading be changed to Nonnegative integer exponents and the beginning to:
&c
This is to emphasize that is a possible definition rather than a matter of religious faith. I request your comments. Bo Jacoby ( talk) 08:31, 22 November 2012 (UTC).
Quondum, are you for or against the suggested change? Bo Jacoby ( talk) 21:56, 22 November 2012 (UTC).
I think everything regarding 0^0 is covered perfectly well in that section, and there is no need to rehash the discussions that already led to the current state of the article. — Carl ( CBM · talk) 23:29, 22 November 2012 (UTC)