How can I prove $a$ had infinite order $\Rightarrow$ $f(a)$ has infinite order?
56234
Isomorphism $f$ preserves the order of an element?
131163
There is a well ordering of the class of all finite sequences of ordinals
127656
How to prove that if $A$ is infinite and $B$ is finite, then $|A\cup B|=|A|$?
53707
Prove that if $A$ is an infinite set then $A \times 2$ is equipotent to $A$
57193
Prove that $f$ has derivatives of all orders at $x=0$, and that $f^{(n)}(0)=0$ for $n=1,2,3\ldots$
22575
Prove that $\lim\limits_{n\rightarrow\infty} \left(1+\frac{1}{a_{n}} \right)^{a_{n}}=e$ if $\lim\limits_{n\rightarrow\infty} a_{n}=\infty$
37398
Proof that$ (a+A)\cap A=\varnothing$ if $A$ is countable
21879
Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A
92376
Let $f:A \rightarrow B$ and C ⊂A. Define f[C]={b∈B: b=f(a) for some a∈C}. Prove or disprove each of the statement
67483
Show that $|a-b|<\epsilon \Rightarrow |a|<|b|+\epsilon$
99633
Let $α$ be an ordinal and $A$ be a set of ordinals. Then $\sup\limits_{β∈A} (α+β) = α+\sup\limits_{β∈A}(β)$
83798
Does $A$ a UFD imply that  $A[T]$ is also a UFD?
32965
Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
146421
How to prove a total order has a unique minimal element
61048
Is this a characterization of well-orders?
73454
Prove that $f$ has finite number of roots
54321
Questions about $f: \mathbb{R} \rightarrow \mathbb{R}$ with bounded derivative