Reputation
2,741
Top tag
Next privilege 3,000 Rep.
Cast close & reopen votes
Badges
7 30
Impact
~103k people reached

Apr
12
revised Discrete Math: Inductions
latex
Apr
12
reviewed Approve Householder matrix Uw acts as the identity on the subspace w
Apr
12
reviewed Approve Can I calculate this sum using matrix multiplication?
Apr
11
comment Why do some series converge and others diverge?
Let's for the moment restrict our attention to series with nonnegative decreasing terms. I think about it kind of like this. There are two opposing "forces" pushing on the behaviour of the partial sums of this series. On the one hand, each of the partial sums must be at least as big as as the last one, since we are adding more and more terms. This pushes up on the partial sums. On the other hand, with each term, the increases in the partial sums are decreasing, since the terms are getting smaller. If the series converges, it is because this second force is somehow stronger than the first.
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