Does $(p(0) \wedge (P(n) \implies P(n-1))) \implies P(n) \forall n\leq 0$?
60869
Is induction valid when starting at a negative number as a base case?
92876
Prove that $ \lim (s_n t_n) =0$ given $\vert t_n \vert \leq M $ and $ \lim (s_n) = 0$
73375
Show that $\prod (1- P(A_n))=0$ iff $\sum P(A_n) = \infty$
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
42366
Prove $\mathbb{P}(\sup_{t \geq 0} M_t > x \mid \mathcal{F}_0)= 1 \wedge \frac{M_0}{x}$ for a martingale $(M_t)_{t \geq 0}$
152856
Using $p\supset q$ instead of $p\implies q$
34478
If $P(A \mid E) > P(B \mid E)$ and $P(A \mid \neg E) > P(B \mid \neg E)$, then is $P(A) > P(B)$ true?
32525
If $f(1)=1$, then is it true that $f(n)=n$ for all $n \in \mathbb{N}\cup\{0\}$.
104500
find a sequence converging to zero but not the element of lp space for every 1<_p<infinity
84021
How can we show that $\varphi(a) \neq a +1$ for every $a \in A$?
45370
Is it true that $|d(x, z) - d(y, z)| \leq d(x, y)$ and how do I prove it?
103732
Proving that for $n \equiv 0 \pmod{2}$, we get ${n \choose 0} < {n \choose 1} <\ldots< {n \choose n/2-1}<{n\choose n/2}$ etc.
71717
Is this always true: $P(A|B) = 1-P(A^c|B)$?
3599
show that if ${a_n} \to a$, and $a>0$, then $\exists N$ such that $a_n>0$ for $n \ge N$.
51687
Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
139537
Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $