1^infinity

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?

0 times anything is 0, even an idea like infinity.
for example, 0 x ice cream = 0

0 times infinity isnt 0

Right, 0*ice cream isn't 0, as ice cream isn't a logical application of the 0.

infinity breaks a lot of rules because its not a number.

For example, y=1/x + 1 can never equal 1.

Every number you plug into x, y will never become 1... unless x is infiinty.

How is 0*ice cream not 0? You have zero ice creams, therefore you have zero. Ice cream is perfectly finite, so it doesn't break any rules.

And in regards to the original question... yeah, it's more or less resolved.

But...

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

That only proves than ln(1^infinity) is undefined.

How is 0*ice cream not 0? You have zero ice creams, therefore you have zero. Ice cream is perfectly finite, so it doesn't break any rules.

Even if you argue that way, you can't just drop units.

It's not equal to zero, it's equal to zero ice cream. You can measure the number of ice cream but it's still a number of ice cream, not a number.

How can people just bring up a storm of conversation about this stuff? I guess it is rather mind-boggling, such as having a two-variable function at (0,0) evaluating to 0 OR 1, depending on how you approach it! (with limits, duh)

The mathematical KajitiSouls says 1^infinity is undefined.

The realist KajitiSouls doesn't care, because 1^infinity doesn't come up in applicable life.

The "curious about black holes" KajitiSouls points out that physics and shyts start not making sense when you combine the really massive with the really small.

Right, 0*ice cream isn't 0, as ice cream isn't a logical application of the 0.

infinity breaks a lot of rules because its not a number.

For example, y=1/x + 1 can never equal 1.

Every number you plug into x, y will never become 1... unless x is infiinty.

1/infinity is not 0, but will go towards 0.

Infinity is not a number, but a concept. It is not a real number.

For example, 1^x=1. 1^infinity, as I mentioned before, is like 1^ice cream cake, since neither is a number. Mind telling me what 1^ice cream cake is? Exactly.

0 is the same thing. Normally 0^x=0. However, 0^infinity=/=0, and if you need an explaination, see the paragraph above.

1^infinity doesn't exist. The limit of 1^x as x approaches infinity is 1. 1 is being multiplied by itself infinitely, and the result is always one. I dunno why everyone keeps proving different things.

The problem is with limits like e=(1+1/x)^x. Here, you have a number that is approaching one being taken to the power of a number that is approaching infinity. This is the most common application of the scenario 1^infinity, in which the base does not actually equal 1 and the exponent does not actually equal infinity, but both numbers approach their respective goals. I believe this is the reason your teacher told you 1^infinity does not equal 1.

The reason this does not equal one is because any number that is greater or less than one will rapidly diverge from one. 1.000000000001^(10^20) is a very large number, even though the initial number was very small. 0.9999999999^(10^20) is a very small number that is close to zero, even though the initial number was very close to one. This is why the limit of any number that approaches one to the power of any number that approaches infinity is undefined, or in mathematically incorrect but simpler terms, 1^infinity is undefined.

This is why the limit of any number that approaches one to the power of any number that approaches infinity is undefined, or in mathematically incorrect but simpler terms, 1^infinity is undefined.

I'd still like to point out that all of you have done a fantastic job of beating around the proper answer to the question. You've all stated that 1^inf is undefined, which i won't argue. It's true after all. But the question is, why isn't it 1 when it seems logical that the answer SHOULD be 1?

"Because it's undefined" is really a bad attempt at getting around it. You guys continue to preach this, but never give a proper answer to why logic doesn't make sense. I'll refer the original poster to my earlier post on page 1 for the proper answer.

P.S. oh, and also because its undefined >> [/sarcasm]

I'd still like to point out that all of you have done a fantastic job of beating around the proper answer to the question. You've all stated that 1^inf is undefined, which i won't argue. It's true after all. But the question is, why isn't it 1 when it seems logical that the answer SHOULD be 1?

"Because it's undefined" is really a bad attempt at getting around it. You guys continue to preach this, but never give a proper answer to why logic doesn't make sense. I'll refer the original poster to my earlier post on page 1 for the proper answer.

P.S. oh, and also because its undefined >> [/sarcasm]

What the pineapple? Did you not read my post? I explained it better than you did. Refer to the entirety of my third paragraph.

Or maybe I should bold the rest of my post, because you ignored everything but those five words. In writing, those bolded words are known as a conclusion. A conclusion should not provide further evidence, nor should it explain anything you haven't touched on previously. I claimed that 1^infinity is undefined because of what I said previously, not as a standalone statement. Not only does your self-serving, dismissive post does not contribute to the discussion, you can't even be bothered to read my post before attacking me.

I'd still like to point out that all of you have done a fantastic job of beating around the proper answer to the question. You've all stated that 1^inf is undefined, which i won't argue. It's true after all. But the question is, why isn't it 1 when it seems logical that the answer SHOULD be 1?

"Because it's undefined" is really a bad attempt at getting around it. You guys continue to preach this, but never give a proper answer to why logic doesn't make sense. I'll refer the original poster to my earlier post on page 1 for the proper answer.

P.S. oh, and also because its undefined >> [/sarcasm]

Well, the issue is that even if you multiply 1^infinity, the number you have will be.... 1^infinity.

0.99999999999999999999999^infinity will go towards 0.00000000000000000000001^infinity after some time, and in the end towards 0, but it will never be zero, and the number we get isn't something we can write. it's like the last part of 1/3 in decimal, or 1/7 for that matter.

This just in from my university professor:

1^inf can't be worked on because you can't be sure how the symbol inf, relates to numbers. Interestingly enough though:

lim x-> inf (1^x) IS actually 1.

This is because as X becomes larger, you're value will still be 1. This you are taking the limit of a fixed number, meaning your end limit will still be 1.

There's some food for thought :3