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I would expect almost NO numbers are rational (integer or fraction) with an infinite number of Reals between each.
by tejtm 1y ago
I would expect almost NO numbers are rational (integer or fraction) with an infinite number of Reals between each.
- JadeNB 1y ago> I would expect almost NO numbers are rational (integer or fraction) with an infinite number of Reals between each. You're right (technically correct, which is the best etc.)! That is why "almost all" can mean everything except rational numbers.
- noqc 1y agoin between any two real numbers, there is a rational number, and vice versa.
- concordDance 1y agoAnd yet somehow there are infinity times more reals than rationals... Very hard to get your head around!
- noqc 1y agoAn fun, immediate, horrifying, consequence. If I remove n elements from R, the remainder has n+1 connected components. The complement of Z in R has |Z| connected components. The complement of Q in R has |R| connected components.