Why is $\forall x \in A:P(x)$ equivalent to $\forall x (x\in A \to P(x)) $?
70166
Why is the universal quantifier $\forall x \in A : P(x)$ defined as $\forall x (x \in A \implies P(x))$ using an implication?
106091
Showing $\mathcal{P}(X)$ is isomorphic to $2^X$
49453
Why do I have to solve for $x$ in this proof, if I choose not to find a counterexample?
152856
Using $p\supset q$ instead of $p\implies q$
79734
Is every sub-lattice of $\mathcal P(X)$ isomorphic to a sub-lattice of $\mathcal P(X')$ containing singleton sets?
132532
Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$
62172
Why does $-b < a < b \iff |a| < b$?
38242
Explicit bijection between the successor of $\alpha$ and $\alpha$ (infinite ordinal).
1027
Why is this true? $(\exists x)(P(x) \Rightarrow (\forall y) P(y))$
25171
Why does a convex set have the same interior points as its closure?
154913
Are all the norms of $L^p$ space equivalent?
112049
How many elements does $\mathcal{P}(A)$ have?
107215
Is $\emptyset \in \emptyset$ or $\emptyset \subseteq \emptyset$?
83714
$A \in B$ vs. $A \subset B$ for proofs
124742
P(A|C)=P(A|B)*P(B|C)?
99458
Suppose $\int_{[a,b]}f=0,\text{ then }f(x)=0 \forall x\in[a,b]$
137511
Trying to show that $\sup \{b^p:p\in Q,\;0<p<x\} = \inf\{b^q:q\in Q,\;x<q\}$