Injective function from reals to irrationals?
54496
Showing that $\mathbb{R}$ and $\mathbb{R}\backslash\mathbb{Q}$ are equinumerous using Cantor-Bernstein
11069
Deciding whether $2^{\sqrt2}$ is irrational/transcendental
128911
Continuous extension of a real function
92734
Existence of a sequence of continuous functions convergent pointwise to the indicator function of irrational numbers
47992
Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
124535
continuous function from $[\pi,2\pi]\to \mathbb{R}^2$
121708
$S := \{x \in \Bbb R^3: ||x||_2 = 1 \}$ and $T: S^2 \to \Bbb R$ is a continuous function. Is $T$ injective?
5803
Produce an explicit bijection between rationals and naturals?
60399
Definition of injective function
111990
Continuous function from $(0, 1]$ onto $(0, 1)$?
23752
Proving Irrationality
114650
In Cantor's Diagonalization Argument, why are you allowed to assume you have a bijection from naturals to rationals but not from naturals to reals?
153969
The "elements" of a real number
3801
Functions that take rationals to rationals
77944
Injective functions with intermediate-value property are continuous. Better proof?
3790
Rational + irrational = always irrational?
5375
Is there a bijective function mapping Natural numbers to Natural numbers, other than $f(n) = n$?