How to calculate total combinations for AABB and ABBB sets?
Apr 19, 2022 · Although both belong to a much broad combination of N=2 and n=4 (AAAA, ABBA, BBBB...), where order matters and repetition is allowed, both can be rearranged in different …
Uncountable vs Countable Infinity - Mathematics Stack Exchange
My friend and I were discussing infinity and stuff about it and ran into some disagreements regarding countable and uncountable infinity. As far as I understand, the list of all natural …
elementary number theory - Common factors for all palindromes ...
For example a palindrome of length $4$ is always divisible by $11$ because palindromes of length $4$ are in the form of: $$\\overline{abba}$$ so it is equal to $$1001a+110b$$ and …
Use the pumping lemma to show that the language is not context …
Nov 13, 2020 · The pumping lemma would be used to show that the language is not context-free. To show that it is context-free, design a context-free grammar that produces it; for this …
random variables - probability of playing music player on shuffle …
1.How many sequences of 4 songs are there where no song plays twice in a row? If we label the songs {A, B, C, D}, then examples are ABCD and ABAB but not ABBA. For this problem I just …
How do we prove that $a^ {\log {b}} = b^ {\log {a}}$ for $a > 1
I have tried using the change of base formula, but can't quite complete the equality: $$ a^{\\log{b}} \\\\ a^{\\frac{\\log_a{b}}{\\log_a{a}}} $$ How do I get the base of the exponent to be b?
11 | abba, where a and b are the digits in a 4 digit number.
Nov 21, 2013 · Truly lost here, I know abba could look anything like 1221 or even 9999. However how do I prove 11 divides all of the possiblities?
How to find period of this periodic function?
Dec 26, 2012 · A different function with zero spacing pattern ABAB might have period $\pi$. If extended, the ABBA pattern is ABBAABBAABBA.., and there are no periods of less than four …
prove $\\Gamma(a)\\Gamma(b) = \\Gamma(a+b)B(a,b)$ using …
Jun 23, 2022 · Are you required to make it wiht polar transformation? Because with the change $x=uv$ $y=u (1-v)$ it's easier
The commutator of two matrices - Mathematics Stack Exchange
The commutator [X, Y] of two matrices is defined by the equation $$\begin {align} [X, Y] = XY − YX. \end {align}$$ Two anti-commuting matrices A and B satisfy $$\begin {align} A^2=I \qu...