Double space after a period at the end of a sentence

Simply put, the "two space" rule is a typesetter's convention. It was developed for use with monospace fonts, so that your eye could easily pick up the start of a new sentence. With modern proportional fonts the double space is largely irrelevant. Further, modern typesetting software uses interword spacing to make the display of text more pleasing. Thus double spacing can make the layout less pleasing.

So my suggestion is: use two spaces if you're banging away on your Mom's old Underwood, but use a single space in any electronic format, unless you're deliberately using Courier for some ungodly reason.

In the early days of the typewriter, every letter was the same size. It was all like this. If I type some more bla bla bla bla bla you'll begin to see (actually it's hard to see on a computer screen, but find some old typewritten text or something and look at it) that often times the spaces between letters and words line up creating what's called "rivers" running down the page. This can get distracting and cause the eye to just "skip over" bits of text. If you read a really long document, before long you would find yourself unconciously running sentences together as you missed periods.  To stop this, writers started putting two spaces after periods to "break things up".

This caught on and became the accepted standard. Then came word processors with their pretty non-monospaced fonts. You'll notice that there are no "rivers" in normal computer text, because the letters are different sizes. The eye can read them more easily. However, a lot of typers still put two spaces after periods, which tends to just look dumb with a nice font. The computer is not a typewriter. There is some evidence that this is why HTML does not allow multiple spaces. (to do that anyway, type   wherever you want a space.)

Pack my box with five dozen liquor jugs.
Pack my box with five dozen liquor jugs.

Note that the upper sentence (made up of every letter in the alphabet) takes up less space than the lower sentence. This is because the upper font has letters with different spacing and the lower font is monospaced.

Therefore, you are both correct. In typing on a typewriter, use double spaces after sentences. On a computer, use a single. I'm a tech writer, and all of the contracted manuals I wrote required the new computer standard (single-spaces between sentences).

Hope this helped.