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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 What is wrong in this proof?
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 suggested edit on 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 suggested edit on 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?