Vlorbik's Diner

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A Isn’t a

Posted by vlorbik on November 12, 2009

Symbolic Logic as Beginning Algebra

We’re {\it reasoning}
already as soon as we’re doing math
of {\it any} kind… and {\it algebraic}
reasoning is going to involve looking
at certain (so-called) strings of symbols.
What better symbols to {\it start} on,
then, in Beginning a course of study of
Algebra, than the symbols created for
discussions of {\it reasoning itself}:
the language of {\bf Symbolic Logic}?

The “usual” way of introducing Algebra
of course uses the symbolism of
Real Number Arithmetic.
This frequently leads to considerable
difficulties due to the astonishingly
rich structure of the Real Number
field.

Working with an {\it un}familiar
symbolism is a tremendous
advantage if it were only for
the ability to wipe out
forest-and-trees issues
like “is multiplication
really repeated addition?

at a stroke. This is to say
nothing of having “routed
around” such commonplace
anxieties as “I’ve never
been very good at fractions
“.
Already these are very good
reasons to at least experiment
with “logic as introductory algebra”.

But… best of all!… there are {\it two values}
in our base set—{\sc t} and {\sc f} typically, or
0 and 1—as opposed to, well,
infinitely or even continuously many.
We will be able to display
{\it complete} “addition” and
“multiplication” tables:
the results of {\it every possible
calculation} of certain kinds. This clears the mind
wonderfully… for what else but
{\it other} kinds of calculating!

Let us begin.

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One Response to “A Isn’t a”

  1. vlorbik said

    update on the repeated additon flap
    by the ever-awesome #-warrior (jason dyer):
    http://numberwarrior.wordpress.com/2010/02/26/multiplication-is-not-repeated-addition-revisited/

    see also (hat-tip):
    http://mathmamawrites.blogspot.com/2010/02/what-is-multiplication.html
    sue v.

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