The Story So Far
Pretend you are in an applied mathematics class. You missed a few sections - you don't have your notes - and your instructor writes this on the board.
A dutiful - but perhaps confused on material - student, you do your best to reproduce what is written on the board as exactly as possible, including every stray ".", in case there is some hidden meaning you don't understand.
Graded Assignment: Upload a .tex file which, when compiled, produces a PDF identical to the example image.
This assignment is adapted from one by Dr. Kevin Cooper. What follows are his suggestions to help you replicate the image:
The page is produced using LaTeX with a 10pt argument to the documentclass command. Pay particular attention to periods at the end of sentences, math italics, alignments, and places where paragraphs begin and do not begin. Use the leqno option to the \documentclass to move the equation numbers to the left side of the page. The footnote at the bottom of the page can be done using the \footnote macro. The \implies and \iff macros obviously figure into the typesetting.
Spacing issues are less critical; so long as the content is correct, you do not have to position everything precisely as in the document.
To do the footnote, use the footnote command: \footnote{Some footnote}