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Aug
29
comment finding volume of the cone by using the dot product
@harry it's actually $u \angle v$
Aug
29
comment finding volume of the cone by using the dot product
the sine and cosine of the angle between $u$ and $v$ resp.
Aug
27
comment Evaluating $\ln(\cos x))$ using Taylor expansion
you should be using different unknowns, now the $x$ in the $\ln$ expansion is different from the $x$ in $\cos x$
Jul
10
comment How to create circles and or sections of a circle when the centre is inaccessible
and your print screen button doesn't work?
May
19
comment Number of ways to order numbers such that greatest number proceeds smallest number
which is equal to $\frac{n!}{2}$
May
16
comment Proving that all eigenvalues are $0$ bar one.
it's sufficient to prove that all $Ax=a\mathbf{e}$
Apr
17
comment Why does $n^0 = 1$?
there is $$ n^k = \Pi^k_{i=1}i$$ but that relies on $$ \Pi^0_{i=1}i=0$$
Apr
10
comment Visually deceptive “proofs” which are mathematically wrong
result of the assumption that $\sqrt b \cdot \sqrt a = \sqrt{a\cdot b}$ for all reals $a$ and $b$ instead of only for positive reals
Apr
7
comment Visually deceptive “proofs” which are mathematically wrong
all of the answers below rely on a slight bend in a diagonal line which accounts for the missing area
Mar
18
comment Minimum number of different clues in a Sudoku
must resist urge to solve sudoku...
Mar
13
comment What is wrong in this proof?
or a square of a negative number; the logarithm of a negative number, those are the most common but any multivalued function can be used
Mar
4
comment For all square matrices A and B of the same size, it is true that (A+B)^2 = A^2 + 2AB + B^2
@Nicholas because distributiveness works even when $AB\ne BA$ (it's not related)
Feb
26
comment What are some interesting cases of $\pi$ appearing in situations that are not / do not seem geometric?
isn't this the just the series expansion of $\arctan 1$?
Feb
25
comment What makes a limit 'go away'?
$$\lim_{x\to ∞} f(x)+g(x) = \lim_{x\to ∞} f(x)+\lim_{x\to ∞}g(x) $$ when both limits exist. and $\lim_{x\to ∞} c = c$ so you can extract the $\frac{11}{7}$ from the limit and keep $\frac{e^x}{7}$ inside it.
Feb
6
comment Is it faster to count to the infinite going one by one or two by two?
it doesn't matter how far you count, you are always just as far from infinity than when you started.
Dec
13
comment Expand in factor when even and odd power is given
for $n=2$ there is no factorization unless you go with imaginary numbers $(A+Bi)(A-Bi)$
Dec
6
comment Prove by induction that $5^n - 1$ is divisible by $4$.
@user17762 $25 * 5 = 25 \mod 100$
Nov
18
comment if matrix such $AA^T=A^2$ then $A$ is symmetric?
$AA^T=AA \Rightarrow A^{-1}AA^T=A^{-1}AA\Rightarrow A^T=A$
Nov
6
comment How can I determine that a relation lacks a property without using a counterexample?
you can try to find a contradiction with the assumption that the property holds for all, this proof by contradiction will also allow you to construct a counterexample
Oct
26
comment What is the simplest proof of the pythagorean theorem you know?
@KeshavSrinivasan moreover it's easy to create a contraption like that in real life that proves $a^2+b^2$ is greater or less than $c^2$ by adjusting the depth