James Martini archive

Tag : math (2)

Plugin testing

Categories: Journal
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Published on: August 5, 2018

One of the benefits of coming back to an existing wordpress blog rather than continuing to try to roll my own in github.io is that I can easily piggyback on other people writing plugins to solve the same problems. So far, the Crayon and MathJax-Latex plugins seem to fit the bill.

Testing syntax highlighting

Testing Latex / Math

$$
\begin{align}
J(\theta) &= \frac{1}{m}\sum_{i=1}^{m}Cost(h_\theta(x)^{(i)},y^{(i)}) \\
Cost(h_\theta(x),y) &= -log(h_\theta(x))& y=1 \\
Cost(h_\theta(x),y) &= -log(1-h_\theta(x))& y=0
\end{align}
$$

Reading set notation

Categories: Journal
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Published on: June 25, 2009

So I’ve been skipping my World of Warcraft time and reviewing calculus and differential equations so I don’t get too rusty. I almost immediately ran into an issue “reading” some of the set notation. It’s great because it’s compact and can communicate a lot of information but that doesn’t help if you can’t read it.

Take for example

{(x,f(x))|x∈A}

Doesn’t say much unless you can read it as “the set of all ordered pair x, f of x such that x is a member of set A”. Here are a few quick rules:

{ } denotes the set
( ) denotes and ordered pair
|  “such that”
: also “such that” just in case things were too clear
∈ “is a member of”
∉ “is not a member of”
∪ union of two sets
∩ intersection of sets

So ℕ = {|a| : a} reads as “The set of natural numbers is equal to the absolute value of a such that a is a member of set ℤ”. Since ℤ is generally the set of ingeters { … ,-2, -1, 0, 1, 2, … } this means that ℕ = {0, 1, 2, … }

So now I can mostly read set notation again. Now I just need to learn MathML.

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