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2d
comment Linear Algebra - four “true or false” questions about matrices and linear systems
How does your example refute 1? $\;$
Sep
12
comment Demonstration that 0 = 1
@MarcvanLeeuwen : $\:$ The relevance of my previous comment is that justifying the limit of the exponentials would have required expanding them first, rather than just using the limit of the exponents. $\hspace{.89 in}$
Sep
12
comment Demonstration that 0 = 1
@MarcvanLeeuwen : $\:$ So I should perhaps be more specific and say that $\:4\pi in-4\pi^2n^2\:$ is a sequence of non-real complex numbers whose absolute values converge to infinity. $\;\;\;\;$
Sep
12
comment Demonstration that 0 = 1
@MarcvanLeeuwen : $\;\;\;$ $4\pi in-4\pi^2n^2$ is a sequence of complex numbers $\hspace{1.89 in}$ whose absolute values converge to infinity. $\;\;\;\;\;\;\;$
Sep
11
comment Demonstration that 0 = 1
The other problem, which the three current answers do not mention, is that $\hspace{1.88 in}$ e-to-the does not have a limit at complex infinity. $\:$
Sep
7
comment Is the following limit undefined?
It doesn't have to be defined on that kind of set either. $\:$ It just needs to be defined $\hspace{1.51 in}$ on a set that has $4$ as an accumulation point. $\;\;\;\;$
Sep
5
revised How can I accurately compute $\sqrt{x + 2} −\sqrt{x}$ when $x$ is large?
fixed title's grammar
Sep
2
comment Show that $\lim a_n =0$ if $|\frac{a_{n+1}}{a_n}|<1, \forall n$
You can replace the initial lim with limsup. $\;$
Sep
2
comment How can I accurately compute $\sqrt{x + 2} −\sqrt{x}$ when $x$ is large?
@user161825 : $\:$ You used the wrong expression for $\hspace{.03 in}f(x)$. $\;\;\;\;$
Sep
2
comment Show that $\lim a_n =0$ if $|\frac{a_{n+1}}{a_n}|<1, \forall n$
@DavidMitra : $\:$ ... or that with limsup instead of lim. $\;\;\;\;$
Sep
2
comment How can I accurately compute $\sqrt{x + 2} −\sqrt{x}$ when $x$ is large?
I think the three radicals on the "approximately" line should contain $\:x\hspace{-0.03 in}+\hspace{-0.04 in}1\:$ rather than $x$. $\hspace{1.23 in}$
Sep
2
revised Is $1$ a subset of $\{1\}$
corrected symbol
Sep
1
comment How can I accurately compute $\sqrt{x + 2} −\sqrt{x}$ when $x$ is large?
Do you mean $\;\; f(x) \: = \: \sqrt{x+2}-\sqrt{x} \;\;$? $\;\;\;\;\;$
Aug
17
comment Some problems concerning regularity os measures.
That's a very weak "regularity" condition. $\;$
Aug
14
comment The meaning of correlation coefficient and p-value
stats.stackexchange.com $\;$
Aug
11
comment A consistent first-order theory whose impredicative second-order variant is inconsistent
$(\forall y)(\exists x)(x+x = y \: \lor \: S(x+x) = y) \;\;$ is a simple formula that is provably independent of Q. $\hspace{1.01 in}$
Aug
7
comment Countably infinite union
How about for $a$ and $b$? $\;$
Aug
1
comment If R is $(a,b)R(c,d) \iff a+d =b+c$ show that R is an equivalence relation.
More relevantly, one can apply the theorem if $X$ is the semigroup of positive integers. $\hspace{1.42 in}$
Aug
1
comment If R is $(a,b)R(c,d) \iff a+d =b+c$ show that R is an equivalence relation.
As mentioned by Did, using subtraction negates the point of this proof. $\;$
Aug
1
comment Two dice thrown, one comes up 6
No, we want $\: P(D\hspace{.05 in}|\hspace{.02 in}\text{ he saw a 6}) \;$. $\;\;\;\;$