Question

Why is 1^infinity an indeterminate form? Isn't 1 raised to anything just 1?

Answer 1

coz its not 1 to power infinty,,its "tending to 1" to power infinity..clearer ?

Answer 2

no sorry.

Answer 3

and that also tending to infinty

Answer 4

"tending"?

Answer 5

\[1^\infty = 1\]

Answer 6

exactly what i think @waterineyes

Answer 7

yes you can think about 1^(some number) as 1 but infinity is not a number. Imagine trying to do that by hand, you would never get done so you cant conclude that it is true:)

Answer 8

You think??
I believe...

Answer 9

no its not 1

Answer 10

so it's just the presence of infintity and infinity being "indeterminate"?

Answer 11

1 power infinity =1 ..true
but in limits its not 1 power infinity..
its like this x^infinty where x tends to 1..i.e. x is very close to 1 but not exactly one..so its really quite different

Answer 12

thats like saying 1^(dog) is 1

Answer 13

yes mathwiz

Answer 14

dog power!

Answer 15

does that make sense @zzr0ck3r ? haha

Answer 16

Infinity implies a mathematical digit and number and not dog cat etc...

Answer 17

infinty is not a real no. actually.

Answer 18

no infinity does not implie a number, infinity grows with no bound... its not a number

Answer 19

count to it:P and get back to me on that one

Answer 20

i am guessing that's also the reason why zero x infinity is indeterminate? because of the presence of infinity?

Answer 21

Why we use Infinity??
Infinity implies the greatest of greatest number that we cannot imagine or write on paper..
1 raised to the power infinity is always 1...

Answer 22

well and 0, because 45*infinity is not indterminate

Answer 23

no its not lol but you can stick with that

Answer 24

http://www.wolframalpha.com/input/?i=1%5Einfinity&lk=4

Answer 25

why is zero x infinity indeterminate but any other number x infinity is infinity? infinity x infinity is also infinity. why?

Answer 26

zero x infinity is actually something tending to zero times something tending towards infinity.
It is actually the result of two things going in opposite directions (if you get what I mean to say)
1^inf = tending to one raised to a power of something that tends to become very large.
Now if that tending to 1 is actually less than 1, it might end up going to zero as (<1)^infinity = 0. or due to a delicate balance between the two opposite directions, it may level out at a constant value

However, inf x inf is actually large x large which is again large. You don't have that sort of opposing type of behaviour in here. Hence inf x inf = inf

Answer 27

for the same reason that x^0 = 1 as long as x != 0 its a lot to exaplin google it:)

Answer 28

last question. why is 1/infinity = 0? is it because 1/0 = infinity?

Answer 29

its not really 1 / x as x tends to infinity is 0

Answer 30

1/0 is undefined..
the word TENDING is very important

Answer 31

yep, are you in calc yet whiz?

Answer 32

yes. just clearing some misunderstandings. because according to the logic i presented, 0 x infinity should be 1. Math is so confusing isn't it =))

Answer 33

thats says that two things that are in an infinite race finish in finite time(one way to think about it )

Answer 34

well thanks for the help. Now, I feel as if i divided by 0.

Answer 35

you sort of did:)