hardmath

Knoxville, TN

uclue.com

Age: 61

Enjoys programming in Prolog.

Richard O'Keefe: "Prolog is an efficient programming language because it is a very stupid theorem prover."

When I cross the street, I look both ways: up and dn.

5h
comment Is the Square Root of an Inverse Matrix Equal to the Inverse of the Square Root Matrix?
There is a risk of misunderstanding in referring to "the" square root of a matrix, as matrix square roots are typically even less unique than square roots of scalars (where we have a choice of sign in picking a square root).
5h
comment Implicit function theoroem
I'm afraid your "statement" to be shown is unintelligible. In the case that a surface $F(x,y,z) = C$ can be "solved for any of the three variables (let's assume this to be in the neighborhood of some point $(x_0,y_0,z_0)$ on the surface), then any one of the three variables, say $x$, would have partial derivatives via Implicit Function Thm. with respect to the other two, say $y,z$. But in your notation it is unclear what "derivative" is meant.
6h
revised Row reduction and the characteristic polynomial of a matrix
edited tags
6h
revised Row reduction and the characteristic polynomial of a matrix
added example of row operations and computation of characteristic polynomial
8h
comment Borel Measures: Continuous vs. Discrete
@Freeze_S: I recommend that you state your specific assumptions about the underlying topological space, if more generality is required.
8h
revised Calculating a limit with infinitely many terms
minor spelling corrections, improved formatting
8h
reviewed Edit suggested edit on Calculating a limit with infinitely many terms
8h
reviewed Leave Closed Borel Measures: Continuous vs. Discrete
11h
comment What is the most efficient way of determining a date of birth using yes/no questions?
The most obvious arrangement for nine questions would entail a sequence conditioned upon the answers to earlier questions, in a well-known high/low arrangement. With some ingenuity the month could be found with four fixed questions (asked all at once) and the day of month with five fixed questions (also asked at the same time).
13h
reviewed Leave Open Prove that $\sup(A-B) = \sup(A) - \inf(B)$
13h
reviewed Leave Open Why is $y{(\log_a(x))} = \log_a{(x^y)}$?
13h
reviewed Close how to solve these sort of problems
13h
reviewed Close How to prove that $\sup(A\cup B)=\max\{\sup(A),\sup(B)\}$?
13h
reviewed Close Does every linearly independent set of n vectors in $R^n$ forms a basis in $R^n$?
13h
reviewed Close what are the set of integers that verify this congruence equation please.
14h
comment what are the set of integers that verify this congruence equation please.
Please explain how you plan to approach this problem, as for example what theorems do you know or what computations you've carried out to find the solutions yourself.
14h
reviewed Reviewed Evaluating the limit of $\lim_{x\to\infty}(\sqrt{\frac{x^3}{x+2}}-x)$.
14h
comment Evaluating the limit of $\lim_{x\to\infty}(\sqrt{\frac{x^3}{x+2}}-x)$.
Given the lateness of the Answer (about 5 months), perhaps a fuller explanation of the equivalence of the limit is in order. It certainly has quite a different appearance.
14h
reviewed Leave Closed Bridge-crossing puzzle
14h
comment Bridge-crossing puzzle
Very similar to this Question about six travellers instead of four.
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