Take any list of reals - for example, the algebraics: \(\{a_i\}\).
Cover each \(a_i\) with an interval of size \(2^{-i}\).
Total length is 1, but every number in the list is covered.
So every list is incomplete, hence the reals are uncountable.

Corollary: The algebraics are countable, hence there are transcendentals.

Sign in to participate in the conversation

The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!