1,005 reputation
1510
bio website
location
age
visits member for 2 years, 6 months
seen yesterday

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
26
comment $ \theta $ is constructible if and only if $\sin \theta$ is constructible.
@CompuChip let me rephrase; constructing $\sin\theta$ make no sense without a unit length. If you want a length of $a \sin\theta$ then you can take $a$ as your unit length.
Nov
26
comment $ \theta $ is constructible if and only if $\sin \theta$ is constructible.
@CompuChip you'll need some unit length in all cases anyway otherwise $sin\theta$ is meaningless
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
Oct
3
comment Riddle: 1 question to know if the number is 1, 2 or 3
@Oleg567 what would you reply be if I gave you the command to say "no" if your number is 1, "don't know" if your number is 2, or "yes" if your number is 3?
Aug
29
comment Find the trace of the matrix?
the diagonal matrix with distinct numbers on the diagonal fits the description
Aug
14
comment Notations that are mnemonic outside of English
@detly but much less funny
Aug
13
comment Notations that are mnemonic outside of English
the Dutch "sokkel" means pedestal
Aug
5
comment Why must a function have to have even and odd parts
only caveat is that $f(x)$ and $f(-x)$ must be defined