Real numbers

All the rational and irrational numbers together - every point on the continuous number line, with no gaps.

Depth 1 · Foundation

You know the reals are the rationals plus the irrationals, and that they fill the number line completely.

Depths of understanding

1
Foundation
You know the reals are the rationals plus the irrationals, and that they fill the number line completely.
Opens after
Rational numbers Irrational numbers
2
Deeper
You understand completeness precisely - every bounded, increasing sequence of reals converges to a real.
Master depth 1 first
LimitsCompleteness - the property that makes the reals gap-free - is stated in the language of limits.

What's still between you and Real numbers, depth 1, in the order you can learn it.

Builds on

This concept

Opens up

Once you know Real numbers, come back to these — they'll mean more.