is 1 to the power infinity defined?

Question

and add your views on how u learned calculus first time ?
(if u did...)

Answer 1

i don't agree with the rest of you. the whole point we apply limits as a variate tends to infinity is that it cannot be defined in the usual, rigorous way. you can look at the limit of 1^n as n->oo which is indeed 1 but the expression 1^oo is not defined.

in fact, the use of limits is one of the most fundamental to the theory of calculus, perhaps the most important concept of modern mathematical theory.

infinity is not a number, 1 to power infinity is undefined. most of the time you have to introduce the concept of infinity through limit notation. With calculus, its best to understand what differentiation and integration are and what kind of problems they are useful for. Then learn the set of rules as well as possible. the trick is to try as many examples as possible and recognise patterns and tricks.

Answer 2

1

Answer 3

you've quite of a level, yet you should understand a number of mathematics is about inference - fairly once you're dealing with infinity. in case you comprehend a million^googolplex = a million, then you definitely can infer that a million^infinity is a million. yet I do see the position you're coming from. I for sure can't call a unmarried human being who has each and every prolonged a million by technique of itself an unlimited type of situations - it really is unquestionably not accessible to attempt this. It surely comes right down to the houses of the quantity a million. considering that a million*a million = a million, then a million*a million*a million = (a million*a million)*a million = a million*a million = a million . it really is a recurrence relation, and as you frame of mind infinity, you're allowed to deduce, by technique of mathematical induction, that the answer will be a million. edit: ok it really is your stepped ahead mathematics, although not very stepped ahead because it really is not needed for this challenge: teach a million^n = a million for any n ? a million Base case: n = a million a million^a million = a million assume the fact holds for n=ok s.t. a million^ok = a million teach that the fact holds for n=ok+a million a million^(ok+a million) = a million^ok * a million^a million a million^ok = a million by technique of the hypothesis a million^a million = a million by technique of the bottom case So a million^ok * a million^a million = a million * a million = a million There. shown by technique of mathematical induction. edit2: So I regarded this up, and that i want to admit that i'm incorrect! a million^? is an indeterminate type. I do, in spite of the indisputable fact that, believe that this would (and could quicker or later) be shown unfaithful. that is accessible that the definition of an indeterminate type must be altered quite. surely, once you try this on Maple, the answer is a million! My evidence doesn't artwork. Induction in basic terms proves for the organic numbers. Infinity isn't a organic volume - that is not a volume in any respect! guy, i think like an fool.

Answer 4

It's defined, and is equal to one by definition.
Also, it seems odd but I first stumbled upon calculus with power series, the only limit I needed was x^n and I could do any calculus problem given, giving the answer as an infinite series of course.
I then tried out Leibniz's limits and found how it could be useful too.

Answer 5

Its simple!! answer is not 1!
Proof:

1 ^ infinity = (2 / 2) ^ infinity = (2 ^ infinty)/ (2^ infinity )= (infinity / infinity )= indefinite

Answer 6

1 multiplied by 1 (squared) equals 1, multiplied by 1 (cubed) equals 1, and so ad infinitum.
hence1 ^ infinity equals 1

Answer 7

the answer is 1..
1 to the power of anything is 1

Answer 8

1^ infinity = 1*1*1*1*1..........
Now go on multiplying 1 to the result.
It will still remain 1, no matter how many times you multiply.

Answer 9

equals 1

Never did calculus, you can see why.

Answer 10

If it isn't defined, it should be.

The answer is 1.