## Proof that rationals are uncountable

Let’s say I have a number q∈Q, i.e. ∀a∈Z.∀b∈N+.q=ab Now I look at a as an endless sequence (a0,a1,a2,…) where ai can be determined by the expression a=∑i=0ai⋅10i and I look at b as an endless sequence (b0,b1,b2,…), where bi can be determined by the expression b=∑i=0bi⋅10i Now I can combine these two sequences into … Read more