Is 1/∞ = 0?

Question

I understand in calculus that the limit of 1/x as x approches infinity is 0. However, can I simply write 1/∞ = 0 or is this against any rules, just like writing 1/0 is undefined.

If it IS possible to write it as 1/∞ = 0, then shouldn't ∞ * 0 = 1? Or 1/0 = ∞? Shouldn't these variations in what should be the same equation be prove in itself that 1/∞ does not equal 0 and is, in fact, undefined?

Answer 1

Yep, you've got it. You can't just say 1 / ∞ = 0 since it's not true. The limit is 0, sure, but not just straight up like you have it written. The answer is undefined.

Answer 2

You are right 1/infinity = 0 but 0/0 and 0/1 are undefined.

Answer 3

yes 1/0= infinity

Answer 4

It is infinitely close to 0, but it is not 0.

No matter how far out you go, the value will approach closer to 0, but because there is 1 unit of it, it can never be 0.

Answer 5

Yes, you are correct. The limit is 0, but it does not = 0.

Answer 6

Try substituting: If { 1/∞ = 0 } then { [ ∞ * (0) ] = [ ∞ *(1/ ∞) ] = 1 }.
But remember that ∞ in a concept and not a tangible entity.

Answer 7

Sorry but the best you do is say is one divided by infinity approaches zero which would seem to imply that zero times infinity approaches one. You have forgotten that infinity is not really a number. Infinity is only a concept and that concept is that numbers do not end. since infinity is not really a number you cannot really multiply or divide by it at all.

Answer 8

1 divided by infinite does not equal zero because in calculus when one writes the limit of 1/x as x approaches infinite equals zero the person is asking what number does 1/x approach as x gets gigantic. This gigantic number is referred to as infinite but is not a number because any number that you plug into x can be very close to zero but not zero. e.g. 1/(10^2,000,000,000,000) = 10^-2,000,000,000,000 but still not zero.

Answer 9

It's not "legal" to write 1/∞ because infinity isn't a number -- it's a concept.

Answer 10

Yes both are undefined