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Comment by solidasparagus | Hacker News Reader

I don't think that's the right way to think about infinity. Just because the chances are infinite and you know goals are possible, it does not mean that there will be infinite goals. There are infinite numbers between 4.0 and 6.0 but only one of them is a prime.

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> There are infinite numbers between 4.0 and 6.0 but only one of them is a prime.

Primality only applies to natural numbers, so there can't be primes between 4.0 and 6.0. There is one between 4 and 6, but that's a finite range.

The concept holds. Perhaps the example isn't great, I'm not sure - but since when does 'the set of numbers between 4.0 and 6.0' not include the natural number 5?

That's a set of real numbers, and primality is not defined for real numbers, so 5.0 can't be a prime. The whole concept is just not applicable unless were talking about natural numbers, in which case the set is finite.

Who said it's the set of real numbers? I don't remember adding any notation that specified the set must be real numbers.

But you can't score 4.1 goals. You can't take 5.9 shots on goal. Goals and attempts are integers. Ask Sheffield United.

I feel like this misses the point. Infinite outcomes != all outcomes.

What you stated is certainly true, but Infinite outcomes == all possible outcomes in infinite quantity, and we know that life is possible.

> infinite outcomes == all possible outcomes in infinite quantity

No it doesn't. This is a common misunderstanding of infinity. Infinite is absolutely not the same as all.

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