Question

Why is 1^infinity not 1?

Answer 1

It is 1...

Answer 2

no

Answer 3

1 to the power of any number is 1...

Answer 4

https://www.google.com/search?q=1%5E93427509827304895720835689273458902733409587620384083452345&gws_rd=ssl

Answer 5

\[1^\infty\] is undefined

Answer 6

huhh.... ???

Answer 7

@ganeshie8

Answer 8

if you are being nitpicky .....


Infinity is not a number .... you can't involve infinity in Math operations.

you have to use limit to express what you are trying to say:
\[\lim_{n \to \infty}1^n=1\]

Answer 9

that makes sense

Answer 10

@chiel140 see infinity is a concept and not a number. Is says that you give me a number, i can give you a bigger number, and it increases without any bounds. If it was a valid number, then the answer would be 1, but it is not a number and hence it is 1^ infinity undefined/. If someone asks you, what is 1^cow, can you say the answer? No, because it is not a number.

Answer 11

ah, ok

Answer 12

thanks :)

Answer 13

1^oo can equal to different numbers, that is why it is indeterminate

Answer 14

the limit is usually defined in a case by case basis, you have to do some kind of logarithm argument . but there are different limits

Answer 15

@PaxPolaris i think the lim 1^n , as n-> oo is 1

Answer 16

but, \[\lim_{x \rightarrow \infty}(1+1/x)^x=e\]

Answer 17

right, thats why its indeterminate

Answer 18

lim (1 + 1/x ) ^(2x) = e^2

Answer 19

It's so hard to understand infinity

Answer 20

1 / infinity = 0 , always , doesnt matter the type of infinity

Answer 21

you just have to memorize a few indeterminate forms

Answer 22

oo/oo , 0/0 , oo - oo , 0^0, and 1^oo

Answer 23

what about oo^0 ?

Answer 24

oo^0 doesn't make sense

Answer 25

wait

Answer 26

lim n ^(1/n) , n -> oo

Answer 27

\[\lim_{x \rightarrow \infty}x^{1/x}\]

Answer 28

the limit of 1/n IS 1, correct.

Answer 29

lets use n

Answer 30

ok

Answer 31

@chiel140 in this kind of situations we generally take logarithms and check if 'Hospital is applicable or not

Answer 32

oo/oo , 0/0 , oo - oo , 0^0, 1^oo , oo^0

Answer 33

now try to find me another one (i dare you )

Answer 34

:p I don't think I can

Answer 35

the rest of the combinations are not indeterminate

Answer 36

oo/0 is not indeterminate, do you see why?

Answer 37

a/0 ... ha!

Answer 38

because
oo/0 = oo * 1/0 = oo * (+/- oo )

Answer 39

right 1/0 -> +/- oo ,

Answer 40

oo/0 = oo * 1/0 = oo * (+/- oo ) = +/- oo^2 = +/- oo

Answer 41

infinity * infinity = infinity
infinity + infinity = infinity

infinity - infinity = undefined

Answer 42

yeah

Answer 43

- infinity - infinity = -2* infinity = - infinity

Answer 44

-infinity + infinity = undefined

Answer 45

this is an infinite conversation.:P

Answer 46

these are infinity rules for limits (it may not be valid in other contexts)

Answer 47

\[\lim_{x \rightarrow \infty} x ^{1/x}=e ^{\lim_{x \rightarrow \infty }\ln(x)/x}=e ^{\lim_{x \rightarrow \infty }1/x}=e^0=1\]

Answer 48

is that correct?

Answer 49

@Princer_Jones

Answer 50

yes it is correct.

Answer 51

:) thanks