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Squirtle, squirtle......


5h
comment L'Hopital's Rule, Factorials, and Derivatives
Sorry its $\Gamma(n+1)=n!$ for $n\in \mathbb{N}$ so it's $\Gamma(1.5)=(\frac{1}{2})!$ (when we abuse notation). In the above comment I abused the abused notation.
5h
comment L'Hopital's Rule, Factorials, and Derivatives
Of course it is not continuous over $\mathbb{R}$, because its not defined for non-integer values. Often physicists (and some mathematicians) will talk about defining things like $(\frac{1}{2})!$ but in fact this is abuse of notation and what they are really talking about is the gamma function as it acts on rationals (in this case $0.5$).
5h
revised showing that l2 norm is smaller than l1
added 12 characters in body
6h
comment L'Hopital's Rule, Factorials, and Derivatives
The comment above is about as good as you can hope for. Derivatives are a tool from calculus, for a derivative to exist the function must (at least) be continuous (over $\mathbb{R}$); because the factorial function is define over $\mathbb{N}$ we need a sensible way to define the notion of a derivative via a good extension to $\mathbb{R}$, the gamma function is just that.
1d
comment Can you cancel out a term if equal to zero?
This really is an awesome answer. $0=0 \not \implies 3x=6$
Oct
17
comment Why is the outer measure of the set of irrational numbers in the interval [0,1] equal to 1?
Why is "the" outer measure.... You should say, why is an "outer" measure of.... Unless you are very specific what sort of outer measure you are using, it's NOT obvious
Oct
17
reviewed Approve suggested edit on Inequalities - x^2 - 1/2 x - 5 < 0 ; why is x > 2 1/2?
Oct
14
revised Basic question on logic
edited title
Oct
14
revised Let $X$ and $Y$ be Banach spaces, show that if they are isomorphic, then $X$ is reflexive iff $Y$ is reflexive.
deleted 1 character in body
Oct
14
comment Why T commutes with $(T-\lambda I)^k$
Pick a $k$, any $k$, and this is true.
Oct
14
answered Why T commutes with $(T-\lambda I)^k$
Oct
14
comment convergence problem in space of sequences
You might just need to read this: math.stackexchange.com/questions/437287/…
Oct
14
comment Showing finite lattices are isomorphic to their sets of ideals.
You say contrapositive.... do you mean contradiction?
Oct
14
comment Prove that the sum of a trigonometric series has bounded variation
Partition your function carefully
Oct
14
revised Prove that an upper triangular matrix $A$, such that $A^*A = AA^*$, must be diagonal.
added 2 characters in body; edited title
Oct
13
comment A monoid with left identity and right inverses need not be a group
Looks to have gotten worse after the edit
Oct
13
comment A monoid with left identity and right inverses need not be a group
What's $b$ if $\{a,e\}=G$?
Oct
13
comment A monoid with left identity and right inverses need not be a group
I think that the following is a really good start: math.stackexchange.com/questions/507279/…
Oct
13
revised Let $X$ and $Y$ be Banach spaces, show that if they are isomorphic, then $X$ is reflexive iff $Y$ is reflexive.
added 6 characters in body; edited title
Oct
13
comment Let $X$ and $Y$ be Banach spaces, show that if they are isomorphic, then $X$ is reflexive iff $Y$ is reflexive.
By symmetry, of course, we get the converse.