One to the power of infinity, e or 1? | Forums

[XyZspineZyX]

We all know that lim of (1+1^x)^x as x increases without bound and lim of 1^x as x goes to infinity can be said as 1 to the power of infinity (gotten from the subtitution of x to be infinity as the rule of limit applies in standard circumstance). Alright, but we all also have known that the former is equal e, and the latter equal one. So, we have the first, one to the power of infinity is equal e, and the other one is equal 1. Any meaningful thought on this matter? My mind has been full of it lately.

[XyZspineZyX]

We all know that lim of (1+1^x)^x as x increases without bound and lim of 1^x as x goes to infinity can be said as 1 to the power of infinity (gotten from the subtitution of x to be infinity as the rule of limit applies in standard circumstance). Alright, but we all also have known that the former is equal e, and the latter equal one. So, we have the first, one to the power of infinity is equal e, and the other one is equal 1. Any meaningful thought on this matter? My mind has been full of it lately.

[XyZspineZyX]

the loneliest number,

of course its one,


but if you ask wit he'll say "isn't it obvious, its 42"




<marquee loop="infinite" width=500><font color=00FF00>0010001001101111011011100110010100100 00001110100011010010110110101100101001000000110000 10111010000100000011000100110000101101110011001000 01000000110001101100001011011010111000000101100001 00010001011010101001101100011011100100111010101100 0100110001001110011</font></marqee>

Message Edited on 10/12/0307:59PM by Spinnaker

[XyZspineZyX]

Fix your sig, Spin [img]/i/smilies/16x16_smiley-very-happy.gif[/img]

-



A single death is a tragedy; a million deaths is a statistic.

Joseph Stalin


Death is nothing to us, since when we are, death has not come, and when death has come, we are not.

Epicurus

The Forum Emperor

[XyZspineZyX]

1^1=1.
1^2=1
1^3=1
1^4=1
1^5=1
1^6=1
1^7=1
1^8=1
1^9=1
1^x=1
x could be any number. No matter how many times you multiply 1 by itself, it's not going to change.

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[XyZspineZyX]

You can't just say that it's to be equal one, since on those both circumstances (two limits that I've mentioned on my first post), both are equal 1^infinity, if you are doing it algebraically, but on the other hand, we all know the fact that lim of (1+1/x)^x as x gets increased without bound is e (2.72.....) and the lim of 1^x as x goes to infinity is equal one. Those two limits are suggesting 1^infinity, but they're not equal. The conclusion that can be derived from this is either it's undefined, or unfound.

[XyZspineZyX]

undefined seems to fit a multitude of situations

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[XyZspineZyX]

Got some interesting facts from Dr. Math:

The question:
"We feel that 1^infinity = 1, infinity^0 = 1, and 0^0 = 1. Part of these conclusions come from the fact that 0^infinity = 0 and 0^(-infinity) = infinity. Could you please explain these determinate and indeterminate forms?"

The answer:
"These forms are called indeterminate because if you replace 1, 0, and infinity by functions the limits of which are 1, 0, and infinity as x -> 0, then the limit of the compound function does not exist, in the sense that the limit depends on which functions you choose."


http://mathforum.org/library/drmath/view/53660.html

[XyZspineZyX]

I think it's not a real number.

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[XyZspineZyX]

That's also the problem. When we deal with infinity, we're dealing on what you might want to call a not real number. Limit is only to find a certain y-value (could be anything, but let just say it's y) as x gets closer and closer to a certain number. It's not to say that x is exactly that number. That's why whenever we have "0/0" on limit, we can reduce them out, as it's not really a "0/0" but so damn close to it, as though it could be assumed as it, but it's still not.