updates
Why don't we use base 6 or 11?
Another question on this site asks why we have chosen our number system to be decimal base 10. There are others asking basically the same thing as well. I...
Read Journal Category
Updates
updates
Definition of $L_\infty$ norm
Where does the definition of the $L_\infty$ norm come from? $$\|x\|_\infty=\max \{|x_1|,\dots,|x_k|\}$$
Read Journal
updates
Localization commutes with Hom for finitely presented modules
I am trying to solve an exercise given in Vakil's Algebraic Geometry notes. Suppose $M$ is a finitely presented $A$-module. The $M$ fits inside an ex...
Read Journal
updates
Number of five-letter words that use letters from the set $\{A, B, C, D, E\}$ and contain exactly three different letters.
I'd like to see if what I did below makes sense. We are not allowed to have words like $ABCDE$ because the words must contain exactly three different...
Read Journal
updates
I have a hard time understanding why $\ln e=1$
I have a hard time understanding why $\ln e=1$ Can someone explain to me why the natural logarithm of e is exactly equal to the first nonzero but positive...
Read Journal
updates
Inverse of natural log
I have a problem: Let $f(x)=\ln(x)$ solve each of the following equations for $x$. the question is in three parts $(f(x))^{-1}=5$ $f^{-1}(x)=5$ $f(x^{-1})...
Read Journal
updates
How to decompose a vector into non orthogonal components?
How to decompose a vector into non orthogonal components? I have a vector with coordinates (-4 , -1). I know how to decompose it into orthogonal component...
Read Journal
updates
What do Greek Mathematicians use when they use our equivalent Greek letters in formulas and equations?
Like for example, it's common to use the Greek letter $\theta$ to represent an angle right? So what would a Greek person doing math use to represent ...
Read Journal
updates
Standard playing card deck without jokers: Deal 13 cards. What is the probability at least 1 suit is not present?
Similar questions: What is the probability that 13 cards drawn from a standard deck has at least one card from each suit? Deal 4 cards from a deck. What i...
Read Journal
updates
Can someone explain the root test and when to use it?
Can someone dumb down and explain the root test for the convergence of a series. Also How to identify when to use it and how? my intuition tells me to use...
Read Journal