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Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
elementary-set-theory
functions
discrete-mathematics
What do sine, tan, cos actually mean?
algebra-precalculus
functions
trigonometry
notation
Why is an ellipse, hyperbola, and circle not a function?
functions
conic-sections
Integer function which takes every value infinitely often
functions
discrete-mathematics
elementary-set-theory
How to represent the floor function using mathematical notation?
functions
notation
definition
How is the codomain for a function defined?
functions
terminology
Proof of linear independence of $e^{at}$
functions
linear-algebra
Codomain of a function
functions
definition
Proving that $C$ is a subset of $f^{-1}[f(C)]$
functions
elementary-set-theory
Why aren't the graphs of $\sin(\arcsin x)$ and $\arcsin(\sin x)$ the same?
algebra-precalculus
trigonometry
functions
graphing-functions
How to prove if a function is bijective?
functions
Can a function return itself or take itself as an argument?
functions
elementary-set-theory
Can differentiation be thought of as a function?$ $
functions
derivatives
can any continuous function be represented as a sum of convex and concave function?
functions
convex-analysis
Are the smooth functions dense in either $\mathcal L_2$ or $\mathcal L_1$?
real-analysis
functions
Are two mathematically alike functions equal?
functions
elementary-set-theory
Are there any non-constant "bump functions" in "closed form" whose Fourier Transforms are also in closed form?
functions
fourier-analysis
examples-counterexamples
fourier-transform
big-list
How to find length of a part of a curve?
calculus
limits
functions
Why can a circle be described by an equation but not by a function?
algebra-precalculus
functions
How prove this function $f(x)=x!-x^n$ is injective
analysis
functions
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