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Showing posts with the label Math

Proofs by induction and real-world business needs

While I was a young and eager undergraduate computer science student, I was taught the method of proving things by induction. Basically, it's a way of showing that something is true for some simple cases, and then showing how it can be true for more complicated cases. There are two major parts to it: prove that the base case works, and prove that the inductive case works. I see some applications of that kind of thinking in everyday business. Just because I can manage documents on my own doesn't mean that the way I do things will scale to other people. So, to build a solution that grows with the business, I'd have to show first that it works for me, and then assuming it works for X people, show that it will still work when X+1 people are in the picture. The thing with most inductive proofs is that they show that something is true, or if we map it tightly, it would show that things are possible in business -- that something is computable and knowable. But in real-world conce...

A fix for LaTeX "Missing $ inserted." console message

While I was running pdflatex on a .tex file containing a math expression, I got this error message: Missing $ inserted. Powering through it would evaluate the math expression adequately, but I included a plus sign later in the same sentence. I followed the directions and made it convert to a PDF beautifully by adding a dollar sign at the beginning and at the end of the math expression. (It's not just at the end-of-the-line, like I would normally guess it meant in a Unix environment.) So, what started off as 9*2^4 turned into $9*2^4$ and produced a beautifully formatted PDF. I should also note that Norm Matloff has a great introduction to LaTeX . EDIT: This one's even better. It just took a while to load and I got impatient.