Prove / disprove: if $f(n)=O(g(n))$ then $2^{f(n)}=O (2^{g(n)})$
15089
Big-O: If $f(n)=O(g(n))$, prove $2^{f(n)}=O(2^{(g(n)})$
20964
Proof that $n^2 < 2^n$
128305
$PGL(n, F)=PSL(n, F)$
4991
Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$
76694
Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$
130093
Prove by Induction : $n < 2^n$
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
92784
Intuitive (combinatorial) proof of $2^n=\sum_{k=0}^n {n\choose k}$
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
44906
Use induction to prove that $2^n$ divides $(2n)!$ for any $n\in\mathbb{Z}_{\geq0}.$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
114277
Proving in Discrete Structures Problem that $2^N = \binom{N}{0} + \binom{N}{1} + \binom{N}{2} + \dots + \binom{N}{N}$
115459
Proving this $F_{n+1} \cdot F_{n-1} - F^2_n = (-1)^n$ by induction
45885
If there exist sequence such that $g(x_n)=f(x_{n+1})$, then we have $g(x_0)=f(x_0)$ for some $x_0$
61117
Prove by induction: $n! \ge 2^{(n-1)}$ for any $n \ge 1$
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
68480
Proof by Induction: Prove that $2^n > n^2$, for all natural numbers greater than or equal to $5$