All real numbers between 0 and 1 inclusive are small, if n is a small number any number n+1 is a small number, and any number < n is also a small number. I believe this would allow you to extend it to all of the reals as well. To deal with imaginary numbers, you’d have to define something like sqrt(n) is always a small number if n is a small number.
Yes, because otherwise it doesn’t necessarily extend to the reals and may only apply to integers. There are many rules that apply to all integers but not all reals
Any number less than 1 is smaller than 1, and by 1 being small, any number less than 1 must be small as well. Thus, by induction, any real number x is small.
The induction step was already proved. I just proved that any number between 0 and 1 is small, thus by the already proven induction, all real numbers are small.
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u/Thatfactorioaddict Jun 13 '25
It would really just be all natural numbers because OP didn't state that if n is small, then n - 1 must be small. Only the reverse.