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Math is just another language; the important thing is logic. Joel Send a noteboard - 27/01/2012 09:46:23 PM
Essentially x0-x, where x is just a digit, not a number, will equal a multiple of 9.

That is sort of it, but going the wrong direction. 10x+x=11x; 11x-(x+x)=9x, by definition a multiple of 9. All other numbers between 10 and 99 are either:

10x+x+y, in which case 11x+y-(x+x+y)=9x, still a multiple of 9, or

10(x+y)+x, in which case 10x+10y+x-(x+x+y)=9x+9y, still a multiple of 9.


I understand how it works but had no idea how to express it in full mathematical style like that (hence using x as both a digit and a numeral in my example). You can tell I'm a writer because I try to explain math with words.

Words are fine as long as we maintain logical coherence, but math provides operations a compact symbology facilitating that. "Six nines equal fify-four" is bulkier than 6*9=54, and maths precision is often (but not always) more clear than words. If you are familiar with the "missing dollar" problem (also at the site,) that is an infamous example; mathematically it is no problem at all, but the wording deliberately obscures the operations so a dollar APPEARS "missing." In some ways math can be easier than verbal language because it lends itself to trial and error; it allows experimentation to figure things out in ways words often do not.

Ultimately, words and math both analyze and communicate concepts and behavior logically. Language is routinely used to discuss concrete objects, and math (especially higher math) can get pretty abstract. As long as we consistently observe logical rules either can get to the same places, but the symbolism of each is better suited to some tasks than others.
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