How come 1^(infinity) isn't 1?

[FleshLight]

 

[FallenHero]

it isnt?

1 to the power of anything is one...

 

[FleshLight]

Originally posted by: FallenHero
it isnt?

1 to the power of anything is one...

1^(x)=1

x=all real numbers

 

[So]

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

 

[Frosty3799]

Originally posted by: So
http://mathforum.org/library/drmath/view/53660.html

winnar

 

[RU482]

Originally posted by: FleshLight

Originally posted by: FallenHero
it isnt?

1 to the power of anything is one...

1^(x)=1

x=all real numbers

wouldn't it even work for 1^i ??

 

[ROTC1983]

That is an imaginary number though, isn't it?

 

[orakle]

it comes out to 1 anyway, its just you need to do your limit a different way. usually you get a 1^inf when you have a limit as n->inf of (n / n+1)^n. As n gets big the 1 doesn't matter and you get 1^inf. The way you solve that problem is you say that (n/n+1)^n = e^ln(n/n+1)^n, then move the n exponent down (log properties), giving you e^n*ln(n/n+1), do the limit and get 0 for the ln function, so you have e^(inf * 0) or e^0, which is 1.

 

[puffff]

now the real question is, what is i^infinity (i being sqrt(-1))

 

[Syringer]

Originally posted by: redly1

Originally posted by: FleshLight

Originally posted by: FallenHero
it isnt?

1 to the power of anything is one...

1^(x)=1

x=all real numbers

wouldn't it even work for 1^i ??

Yes.

 

[czech09]

Indeterminant...

 

[Soccerman06]

Because of some rule in calculus, i dont remember what its called, infinity acts as a 0 when used in equations.

 

[FleshLight]

Infinity isn't a real number. Therefore the 1^X=1 rule doesn't apply.

 

[Cristatus]

Originally posted by: So
http://mathforum.org/library/drmath/view/53660.html

:shocked: They have a forum for this kind of stuff?

 

[So]

Originally posted by: logic1485

Originally posted by: So
http://mathforum.org/library/drmath/view/53660.html

:shocked: They have a forum for this kind of stuff?

Apparrently. This was the first google result for "1^infinity"

 

[TallBill]

But the real question is. Why do you have nothing better in your life right now to talk about other then math on an online forum? And why do I have the time to mock you?

 

[dighn]

Originally posted by: TallBill
But the real question is. Why do you have nothing better in your life right now to talk about other then math on an online forum? And why do I have the time to mock you?

math is fun

 

[Soccerman06]

Originally posted by: TallBill
But the real question is. Why do you have nothing better in your life right now to talk about other then math on an online forum? And why do I have the time to mock you?

kinda like posting on AT right?

 

[TallBill]

Originally posted by: Soccerman06

Originally posted by: TallBill
But the real question is. Why do you have nothing better in your life right now to talk about other then math on an online forum? And why do I have the time to mock you?

kinda like posting on AT right?

My point exactly.

 

[MBrown]

Originally posted by: FleshLight
Infinity isn't a real number. Therefore the 1^X=1 rule doesn't apply.

 

[mercanucaribe]

I don't get it. No matter how many times you multiply 1 by 1, it won't be anything but 1.

 

[S Freud]

I hate math :|

 

[FleshLight]

Originally posted by: mercanucaribe
I don't get it. No matter how many times you multiply 1 by 1, it won't be anything but 1.

Most theorems/proofs have the domain of all real numbers. But infinity isn't a real number. It's more of a concept that we'll never understand.

 

[jonnyGURU]

1^(Infinity) > 1^(Acura)

 

[Inspector Jihad]

Originally posted by: jonnyGURU
1^(Infinity) > 1^(Acura)

😀