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Can Infinity Be Less Than One?

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The concept of infinity cannot be comprehended, because infinity is so unimaginably large. But a certain "type" of infinity is actually less than one. (And no, it is not negative infinity.) Think about it this way:

You can have the fraction 1/2. There is also 1/3. And 1/4, 1/5, 1/6, 1/7, etc. The fractions go on to 1/infinity. Isn't it odd to think that an uncountable number can be only a little more than zero?

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• 5 weeks later...

1/n is basically "one divided into n parts"... using this definition, "one divided into an uncountable number of parts" will be naturally close to zero. I think the jump you made was

- infinity is uncountable

- 1/2, 1/3, 1/4.... 1/infinity

- 1/infinity is uncountable (Why? 1/infinity is clearly defined as zero..but let's say I grant you this even if I do not agree)

- infinity is less than zero (Why? just because it is uncountable, it is not infinite )

Cheers!

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• 3 years later...

I think what she means here is that the fractions can continue infinitely but in the end none of the factions are going to be greater than 1.

Technically this is true, if Infinity in number form is an unimaginable amount of numbers, then putting any of those unimaginable amount of numbers under the fraction would never get you above 1 or below zero.

While I was saying this, I figured something out, if you put a fraction which is also part of an Infinity of numbers under 1, that would get you a whole number which is above 1.

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• 2 months later...

Yes the answer to 1+2+3+4+5+....+oo is -1/12

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