1^infinity

My calc teacher says it's undefined.

Someone explain this to me, I don't get it. How is it not just 1?

I would think it would be one, it doesnt matter how many times you multiply one by one, its still one. Then again, I'm 13, thus ignorant.

Inifinity is merely a concept, so basically you're multiplying 1 by itself an unlimited number of times. There is no end, thus there is no product. :. 1^infinity != 1.

Here's a more numberical proof:

Let x = infinity

1^infinity = 1^(x), take the ln of 1^(x) (mathematically legal as long as you raise the answer to e in the end), you get

ln(1)^(x) = xln(1) = ln(1) / (1/x)

take the limit

limit x ->infinity : ln(1) / (1/x)

ln1 = 0
1/x = 0

thus, you have 0/0 which is undefined. Therefore, 1^infinity is undefined.

when you play with infinity, algebraic reasoning doesnt apply. you need calculus tools.

Because infinity/infinity is not defined, because infinity - infinity is not defined, because 0/0 is not defined and because 0^0 is not defined.

Lookie:

1^infinity / 1^infinity = 1^(infinity - infinity) = 1^(undefined)

orrr:
we say that 1^infinity = 1
then infinity is described as = lg 1 / lg 1, which is 0 / 0

0^1 / 0^1 = 0^(1-1) = 0^0 BUT YOU CANT DIVIDE BY 0.

Edit: In theory, if you say that 1^infinity = 1, then you also say that 0^0 = infinity. wat.

Because infinity/infinity is not defined, because infinity - infinity is not defined, because 0/0 is not defined and because 0^0 is not defined.

Lookie:

1^infinity / 1^infinity = 1^(infinity - infinity) = 1^(undefined)

orrr:
we say that 1^infinity = 1
then infinity is described as = lg 1 / lg 1, which is 0 / 0

0^1 / 0^1 = 0^(1-1) = 0^0 BUT YOU CANT DIVIDE BY 0.

Edit: In theory, if you say that 1^infinity = 1, then you also say that 0^0 = infinity. wat.

There's no limit to how many 0's you can divide into 0, so it's 0 or infinite!

There's no limit to how many 0's you can divide into 0, so it's 0 or infinite!

Call x = 0

x/x.
Stroke the x up and down. you're left with 1/1.

But the issue with 0^2 or 0^1 is that you're not really dividing by anything.

funnily enough is that 0^3/0^1 in theory is 0^2, but is not defined.

Call x = 0

x/x.
Stroke the x up and down. you're left with 1/1.

NOT ALWAYS!

(Spanish here, not sure about the math stuff names in english)

what you did is only used with limits. If it's a direct calculation, that doesn't work.

That's because as a limit, it's "almost zero, but not yet". But as a pure zero, it's just indetermination.

Well infinity isn't a number, so it's like multiplying 1^ice cream cake

NOT ALWAYS!

(Spanish here, not sure about the math stuff names in english)

what you did is only used with limits. If it's a direct calculation, that doesn't work.

That's because as a limit, it's "almost zero, but not yet". But as a pure zero, it's just indetermination.

x/x is always 1 unless x is infinity or 0. o.O

but yeah, derivation is using that to find limits and stuff.

http://en.wikipedia.org/wiki/Exponentiat...zero_power
http://en.wikipedia.org/wiki/Division_by_zero

Oh and as a side note, I know it's undefined, but I had a brain-somethingcrazy thinking about the number 0 and how it's like the opposite of infinite.

Oh and as a side note, I know it's undefined, but I had a brain-somethingcrazy thinking about the number 0 and how it's like the opposite of infinite.

Oh, think about it: Infinite is everything, and Zero is nothing... In maths it's like the two sides of the space, since technically, minus infinity meets with positive infinity (most of the times, at least)... like a loop, making those two like one.

Oh and as a side note, I know it's undefined, but I had a brain-somethingcrazy thinking about the number 0 and how it's like the opposite of infinite.

0 exist, theoretically. But nothing doesn't

infinity is the opposite of nothing.

But everything has to have an opposite, or else there's some major imbalances with everything ever... :f6:

Rather than sit here and think about things that don't have any significance I'm going to do what I always do and save it for when I'm having trouble sleeping.

Enjoy your infinite.... wait.. in-finite, finite, that's the opposite if infinte! If something isn't finite it's infinite! 1^Infinite. That satisfies me for now!

But zero isn't finite! Thus, 1^infinite = 1^0 which is 1. Then again, 0 isn't infinity.

Funny stuff, eh?

So after reading through this all I can say is... missed the point much? Sure you guys explained why 1^inf isn't defined but that doesn't technically answer the original question. You never explained why it isn't 1.

Here's your answer OP:

The reason 1^inf isn't defined is because in calculus, limits involving said situation are... well, I'll just show you:

lim x->0 (1+x)^ 1/x
If you straight out plug in zero, you're looking at a situation of 1^inf. You'd think that the answer to this is 1 right?

However,
lim x->0 (1+x)^ 1/x = e ~ 2.71828

Conclusively it can also take on any other number of answers:

ex. 1
lim x->0 (1+x)^ ln 5/x
Once again plugging in 0 gives you another 1^inf situation.

However the answer is 5.

ex.2
in general
lim x->0 (1+x) ^ k/x = e^k

So as you can see, the reason it isn't 1 is because of situations like these. You can make a 1^inf situation give you any positive answer you want.

I hope this answered your question Russt.

P.S. I didn't mean to sound as if the rest of you guys didn't give the right answer. You technically did, but just in the wrong way. While it gave the explanation as to why 1^inf wasn't defined, you didn't say why it wasn't 1 when it looks like it should be 1.

x/x is always 1 unless x is infinity or 0. o.O

You can still find the limiting value though, if you know the relationship between the infinities.

Eg. (2x)/x, if x = infinity then it is infinity/infinity, but as x->infinity it has the value 2.

If Infinity is a concept and not a number, then 0 x *infinity* would not have an answer right? My friend asked me this two days ago actually, and I didn't know the answer so if it's not too far off topic, can somebody explain the answer to me?

Well infinity isn't a number, so it's like multiplying 1^ice cream cake

I laughed for like 10 mins

On topic: It's undefined because infinity is an idea, not a number

Yeah, it's undefined.

eg. let x->infinity
then for any n, n/x -> 0, x->infinity
So, (n/x)*x = 0*infinity = n, and this is true for any real n, so in general 0*infinity is not a specific value o-O