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 Mar 13 answered Composite Relations - Give Examples of relations $R_1$ and $R_2$ such that $R_2 \circ R_1 = R_1 \circ R_2$ and $R_2 \circ R_1 \neq R_1 \circ R_2$ Mar 13 comment Composite Relations - Give Examples of relations $R_1$ and $R_2$ such that $R_2 \circ R_1 = R_1 \circ R_2$ and $R_2 \circ R_1 \neq R_1 \circ R_2$ I suspect that in definition of a relation you meant to write $$R_2 \circ R_1 = \{(x,y) \in S \times S :( \exists \mathbf{v} \in S)[(x,v) \in R_1 \land (v,y) \in R_2]\}$$ rather than $\exists y$. Mar 13 answered Modus operandi for proving Evaluation Fundamental Theorem of Calculus (Abbott p 200, Spivak p 272 T14.2) Mar 13 answered Probability of independent events $P(ab)=P(a)*P(b)$ Mar 13 accepted Can a set containing a single vector from a vector space over a finite field be linearly dependent? Mar 13 answered What does 'finite-valued' mean? Mar 13 comment Can a set containing a single vector from a vector space over a finite field be linearly dependent? Perfect answer, thank you. The question arose from a problem involving finding a minimal set of linearly dependent vectors, so I'm a little sad the answer is no. Mar 13 answered Can $\frac {100-100}{100-100}=2$? Mar 13 asked Can a set containing a single vector from a vector space over a finite field be linearly dependent? Feb 21 revised Domain of an absolute value texed it up Feb 21 comment What happends when you multiply a constant or variable by a trig function? well, what happens when you multiply a constant or variable by 1, a number less than 1 but greater than 0, 0, a number less than 0 but greater than -1, and -1? Now imagine doing that periodically. Feb 21 comment How does this proof of the Cauchy-Schwarz Inequality work? I added an edit to my answer which hopefully answers your question a little bit better. Feb 21 revised How does this proof of the Cauchy-Schwarz Inequality work? added 1116 characters in body Feb 20 reviewed Approve How does this proof of the Cauchy-Schwarz Inequality work? Feb 20 answered How does this proof of the Cauchy-Schwarz Inequality work? Feb 20 comment How does this proof of the Cauchy-Schwarz Inequality work? The maximum or minimum of a quadratic $Ax^2+Bx+C$ occurs at $-\frac{B}{2A}$. In this case, $A=a$ and $B=-b$. Feb 18 answered Is -1 less than 0.1? Feb 10 reviewed Approve Convergence of a telescoping series divided by another series Jan 25 awarded Popular Question Jan 18 accepted Is the construction of $\mathbb{R}$ by Cauchy sequences due to Cauchy? For that matter, are Cauchy sequences due to Cauchy?