READING: II §2 O6
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II §2 O5
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.
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.
on to O7