Full Idea
The set of 'real' numbers, which consists of the rational numbers and the irrational numbers together, represents "the continuum", since it is like a smooth line which has no gaps (unlike the rational numbers, which have the irrationals missing).
Gist of Idea
The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps
Source
Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5)
Book Reference
Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.19
A Reaction
The Continuum is the perfect abstract object, because a series of abstractions has arrived at a vast limit in its nature. It still has dizzying infinities contained within it, and at either end of the line. It makes you feel humble.