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Apr
13
answered Writing Series as a Telescoping Series
Apr
13
reviewed Approve suggested edit on Limited completeness and restricted quantifiers
Apr
13
reviewed Approve suggested edit on Is it possible to triangularize a matrix only by adding scalar multiples of rows to each other?
Apr
13
revised Proof by induction valid or not?
added 1169 characters in body
Apr
13
answered Proof by induction valid or not?
Apr
13
comment For any continuous function f(x), how can I split up the function and restrict the domain to find an inverse?
This is a pretty broad question. You might be better off coming up with one or a few simple examples of problems you want to be able to solve and trying to work through those, maybe with help from this community if you get stuck.
Apr
13
answered basic conditional probability proof
Apr
12
answered Prove $a_n = \begin{cases}1 & \text{if $n=2^k$ for some $k\in N$}\\ 0 & \text{otherwise} \end{cases}$ diverges.
Apr
12
comment When are $\Delta x$, $\delta x$, $dx$, and $\text{đ}x$ exactly the same? When are they approximately the same?
when you write $\delta x$, do you mean $\partial x$?
Apr
12
awarded  Citizen Patrol
Apr
12
revised Discrete Math: Inductions
latex
Apr
12
reviewed Approve suggested edit on Householder matrix Uw acts as the identity on the subspace w
Apr
12
reviewed Approve suggested edit on Can I calculate this sum using matrix multiplication?
Apr
12
reviewed Reject suggested edit on Inverting probability generating function via mellin transform substitution.
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