query: An X is an X is an X
positive_passages.docid: 153369
positive_passages.text: an "X is an X is an X" what does this mean?
negative_passages.docid: 93952
negative_passages.text: Show that $X$ can be represented as a union of disjoint equivalence classes
negative_passages.docid: 41779
negative_passages.text: Is $x/x$ equal to $1$
negative_passages.docid: 121732
negative_passages.text: Functional completeness of $\{\text{or},\text{ xor}, \text{ xnor}\}$
negative_passages.docid: 5639
negative_passages.text: No \xrightrightarrow[a]{b}?
negative_passages.docid: 130998
negative_passages.text: Is $\exists x \in A ~:~ P(x)$ the same as $\exists x ~:~ x \in A \implies P(x)$
negative_passages.docid: 32929
negative_passages.text: Questions about proving $\lnot \lnot a = a$
negative_passages.docid: 49385
negative_passages.text: Proving $\forall x (A\to B) \to(A \to \forall x B):x\notin \mbox{free}(A)$ in a Hilbert system where it is not an axiom
negative_passages.docid: 142993
negative_passages.text: Proof of A ⊆ C and B ⊆ C ⇔ A ∪ B ⊆ C
negative_passages.docid: 154327
negative_passages.text: $A^2X = X$ show that $AX = X$, if $A_{ij} > 0$ and $x_{i} > 0$
negative_passages.docid: 54029
negative_passages.text: What is x after "x = x++"?
negative_passages.docid: 146231
negative_passages.text: Let X be a set with an associative binary operation ◦ with identity e. Suppose every element of X satisﬁes x ◦ x = e. Prove that ◦ is commutative.
negative_passages.docid: 89034
negative_passages.text: For any $\epsilon$, if $\epsilon>0$ and $|x|<\epsilon$, then $x=0$
negative_passages.docid: 122729
negative_passages.text: 'X makes the device operate' or 'X makes the device operates'
negative_passages.docid: 56399
negative_passages.text: Proof for $A \cup B = B$ if and only if $A \subset B$
negative_passages.docid: 101326
negative_passages.text: My teacher describes absolute value confusingly: $|x|=\pm x,\quad \text{if}\enspace x>0 $.
negative_passages.docid: 80209
negative_passages.text: If $X,Y$ are equivalence relations, so is $X \times Y$