Thursday, January 27, 2011

The most important thing in Algebra - Euler

Quote from The Elements of Algebra - Leonard Euler Translated from French by John Hewlett, 1822:
It is of the utmost importance through the whole of Algebra, that a precise idea should be formed of those negative quantities. I shall, however, content myself with remarking here, that all such expressions as
+1 - 1, +2 - 2, +3 - 3, +4 - 4, &c.
are equal to 0, or nothing. And that
+2 - 5 is equal to - 3:
for if a person has 2 crowns, and owes 5, he has not only nothing, but still owes 3 crowns.

If I spend as much money as I earn, then I'll have nothing at the end of the day of the paycheck. If I spend more than I earn, then I'll have not only nothing but also I have to do something extra to make it even that is still nothing.

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