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Apr
25
comment $\sup\limits_{t>0}[\frac{g(t)}{\sup\limits_{t<u<\infty}g(u)}]\leq 1$
To fleshen out the last sentence: Replace $2^{-n}$ with $\frac1{n!}$
Apr
25
answered How can I show that $G$ is non abelian of order 20?
Apr
25
answered You are given two points and a circle. Construct a circle passing through the given two points and tangent to the given circle.
Apr
25
comment $\frac{0}{0}$ Indeterminate
The notion "indeterminate form" relates to the fact that $a_n\to 0$, $b_n\to 0$ does not tell us much about the limit of $\frac{a_n}{b_n}$. Howver, $\frac 00$ is also "undefined" for the simple reason that it is not immediately defined per the usual definition of $\frac ab$ as the unique solution (if it exists) of $b\cdot x=a$. Lacking uniqueness in the case $a=b=0$, this definition does not cover $\frac 00$. -- In contrast to this, $0^0$ is an "indeterminate form" (in the unkown-limit-sense above), but it is defined (contrary to somewhat popular belief)
Apr
25
revised The $\cos(\alpha-\beta)$ formula always need $\alpha > \beta$ or not?
deleted 1 character in body
Apr
25
comment The $\cos(\alpha-\beta)$ formula always need $\alpha > \beta$ or not?
@user3270418 Where do I show the sum formula? I read $\cos(\alpha-\beta)$ in my post.
Apr
25
answered Significance of derivative in finding square free decomposition
Apr
25
answered Deterministic finite automaton parity bit question
Apr
25
comment The $\cos(\alpha-\beta)$ formula always need $\alpha > \beta$ or not?
Are you sure your argument leads to a "No"? - Oh, you seemingly answered the title question, which is the opposite of the body question ...
Apr
25
comment The $\cos(\alpha-\beta)$ formula always need $\alpha > \beta$ or not?
@user3270418 No, I mean what I wrote. For $\alpha=\beta=60^\circ$, we have $\cos(60^\circ)^2+\sin(60^\circ)^2=(1/2)^2+(\sqrt 3/2)^2=1/4+3/4=1$
Apr
25
answered The $\cos(\alpha-\beta)$ formula always need $\alpha > \beta$ or not?
Apr
24
answered Show that there is a step function $g$ over $[a,b]$
Apr
24
comment Is there a way to write an infinite set that contains only irrational numbers without integer multiples?
In the same spirit as the last, $\{\,q\sqrt 2\mid q\in \Bbb Q\cap [1,2)\,\}$
Apr
24
comment The maximum of the absolute value of a real-valued function
You could simply use that $\sup\bigcup_{i\in I}A_i =\sup_{i\in I}sup A_i$
Apr
24
answered Probability of seeing a headlight getting switched on
Apr
24
comment Time complexity for loops
@Manuel kis declared as int, hence can only advance by intsteps. As you used a C-like syntax, I assumed C-like semantics. And there the conversion of 0.01 * 99 to an int produces 0.
Apr
24
comment Equivalence relation and equivalence classes given function and relation
As a matter of fact, this is the easiest and also only example of equivalence relations
Apr
24
answered Question to the proof of: Let $A$ be a finite abelian group and let $g \in A$. Suppose that $\chi(g)=1$ for every $\chi \in \hat A$. Then $g=1$.
Apr
24
answered Time complexity for loops
Apr
24
comment Time complexity for loops
We are interested in the behaviour as $n\to\infty$, but note that the loop will not terminate for $2\le n\le 9$ (and the case $n=10$ may depend on floating point precision). - Same argument for the inner loop if $n\le 99$