### rare MEdZ-related post

i’ve just edited in a subscript-backslash-zero

to the top line…

which now reads …

to repair an *earlier* repair, done sloppily.

somewhere along the line i tacked on the “—{(0,0)}”

*without* adjusting the “zee-cross-zee” ().

a beginner-like blunder, i confess. onward! *more* mistakes!

(just get down in the dirt and *calculate*, by golly.)

anyhow, owners of *Math Ed Zine* #0.4— by name—

should please to adjust the appropriate page in their issues.

which, being interpreted, means that

the set of *rational numbers* (**Q**) can be

represented as the collection of *lines through

the origin* (in the usual *(x,y)*-plane),

having *rational slope*. The slope condition,

for a given line, is equivalent to the condition

that there be an *integer* pair lying on the line

(nonzero; it gets to be something of a pain…).

the algebraic process whereby S…

nonzero-integer-pairs…

“maps onto” **Q**

is called “factoring by a relation”.

the relation in this case is called “tilde” (~).

tilde is defined by

” (x_1, y_1) ~ (x_2, y_2)

MEANS THE SAME THING AS

x_1 * y_2 = x_2 * y_1″

(“cross-multiplication” is in effect;

tilde is the relation we want “because”

when ).

oh heck. there’s that infinite-sloped line.

belongs to S/~, too. OK. modify the .

let’s call it , say. okay.

that’s it.

.

April 10, 2011 at 5:37 pm

we shoulda just had x nonzero

and got it over with…

[

x, not y, because we’re using “slopes”

of the form “(y_2 – y_1)/(x_2 – x_1)”.

]

April 17, 2011 at 10:51 pm

weirder and weirder. i recently found an

issue of the zine wherein i’d *made* the

correction to …

but *without* cutting “zero” out

of zee-cross-zee.

anyhow any and all future printings

will be correcter & very likely prettier

than any’ve been so far.