Tariq on Nostr: There is no natural number between 3 and 4. Why is this? Yes, it sounds obvious, but ...
There is no natural number between 3 and 4.
Why is this?
Yes, it sounds obvious, but what is the precise mathematical reason?
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I'm no expert but my guess is that it is by definition of the naturals, the Paeno axioms, that each natural number n has only one successor n+1, so there can't be another.
My original thought was the naturals are "evenly spaced out" so you can't have anything in between. But this is unsatisfactory as it suggests a richer space eg real numbers.
#maths
Why is this?
Yes, it sounds obvious, but what is the precise mathematical reason?
---
I'm no expert but my guess is that it is by definition of the naturals, the Paeno axioms, that each natural number n has only one successor n+1, so there can't be another.
My original thought was the naturals are "evenly spaced out" so you can't have anything in between. But this is unsatisfactory as it suggests a richer space eg real numbers.
#maths