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seen Dec 16 at 6:38

Mar
13
answered Number of words in containing $0,1$
Mar
13
comment Modus operandi for proving Evaluation Fundamental Theorem of Calculus (Abbott p 200, Spivak p 272 T14.2)
But this clearly does not necessarily hold for all $x\in (t_i - t_{i-1})$'s, so we need to show that there is an $x_i$ in each interval such that it holds. But that is exactly what the mean value theorem promises.
Mar
13
comment Modus operandi for proving Evaluation Fundamental Theorem of Calculus (Abbott p 200, Spivak p 272 T14.2)
@TuckerRapu $f$ can be discontinuous. MVT is a very powerful theorem that you can use to prove all kinds of things about the behaviour of a differentiable function on an interval. As littleO explains, we can get to $g(b)-g(a)\approx \sum g'(x_i)(t_i - t_{i-1})$ for some $x_i$ in the interval without appealing the the mean value theorem. Now we want to tighten that $\approx$ to an $=$, that is, we want to write $g(b)-g(a) = \sum g'(x_i)(t_i - t_{i-1})$...
Mar
13
answered GCD of pairs of integers
Mar
13
revised A difficult equation containing exponent 2 and 3
edited tags
Mar
13
answered A difficult equation containing exponent 2 and 3
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 How does this proof of the Cauchy-Schwarz Inequality work?