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Hopeful mathematics student with some competition level problem solving experience. Studying algebraic topology and algebraic geometry at the moment, but I feel like anyone who know anything know more than I do.


7m
comment Find a basis for the subspace of polynomials of degree 3
What are your own thoughts on this problem?
8h
answered Linear map problem
8h
revised Linear map problem
TeX-ed the pictures
19h
revised “Evaluated at” or “at” notation
added 40 characters in body
19h
answered “Evaluated at” or “at” notation
22h
comment Proving arithmetical properties for non-natural numbers
For fractions, $a^{\frac{p}{q}}$ is defined as $\sqrt[q]{a^p}$ exactly so that those rules still apply.
23h
comment Solve the recurrence relation $x_{n+2} -3x_{n+1} + 2 x_n = n$
Try a second degree polynomial for the inhomogeneous part.
1d
comment What is the right probability?
Have you heard about the Monty Hall problem? This is the Monty Hall problem.
1d
revised What is meant by $(a+ib)^{c+id}$
deleted 4 characters in body
1d
answered What is meant by $(a+ib)^{c+id}$
1d
comment Is it really possible to make all possible numbers with an infinite binary table?
With your table, you'd still have trouble with $\frac{1}{3}$ or $\pi$, just as you would have with normal base ten, but as I said, any whole, positive number works completely fine.
1d
comment Is it really possible to make all possible numbers with an infinite binary table?
Any (positive) integer can be represented like this, in a unique way, but for large integers you might need many places. By the way, if you strip the table and just keep the zeros and ones (like $110$ in your example), you've successfully written down your number in base $2$, or binary.
1d
answered Prove that two matrices A and B have a common eigenvalue if and only if the characteristic polynomial of A evaluated at B is not invertible.
1d
answered How many unique sets do you get if you pair 8 girls and 8 boys?
1d
comment True or false statement
Try with $f(x) = \frac{1}{2}$.
1d
answered Asymptotic equivalence and $\lim_{x\to 0} \frac{\sin x}{x}=1$
1d
answered Probability of a player winning again after i games
1d
comment Continuity of the limit of a function
For any $n$, we have $f_n(0)= 1$, so $g(0)=1$. But for any other $x$, there is an $N$ so that $1/N<x$, and whenever $n>N$, we have $f_n(x)=0$, so $g(x) =0$. Therefore we must have $$\cases{g(x) =1&$x=0$\\g(x)=0 &$x>0$}$$
1d
comment If the sum of the digits of n is equal to the sum of the digits of 5n, then prove that 9|n.
Another example: $n=144$, sum of digits is $1+4+4= 9$. Sum of digits in $5n$ is $7+2+0=9$, so they have the same sum of digits. The theorem then says that $n$ should be divisible by $9$, and it is: $144=9\cdot16$.
1d
comment If the sum of the digits of n is equal to the sum of the digits of 5n, then prove that 9|n.
No, the sum of digits in $45$ is $4+5=9$, which is the same as the sum of digits in $9$. So with $n=9$, you have an example of a number with the property mentioned, and it just so happens that $9$ does divide this $n$, just as it should according to the theorem we wish to prove.