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begin quote ita"
CHAPTER II [:] The Real Number System [...] 2. ORDER. "end quote
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O6:       THE SQUARES OF REAL NUMBERS ARE GREATER THAN OR EQUAL TO ZERO

The square of a real number   a   is denoted by   a²   and is defined to be   a·a.

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For any   a   we have   a²0,   with the equality holding only if   a=0;   more generally the sum of the squares of several elements of     is always greater than or equal to zero, with equality holding only if all the elements in question are zero. For by O5 [positive·positive   and   negative·negative], the statement   a≠0   implies   a²0,   and a sum of positive elements is positive.


Note the special consequence   1 = 1²0.
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on to O7