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begin quote ita"
CHAPTER II [:] The Real Number System [...] 2. ORDER. "end quote
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O7:     THE MULTIPLICATIVE INVERSES OF THE POSITIVE REAL NUMBERS ARE GREATER THAN ZERO
a0 1/a0

Please recall that the division   b/a   is defined to be   b·a.

Consequently, if   b=1   we have   1/a = 1·a = a.

begin quote ita-2-2-12-pg20 "
If   a0,   then   1/a0.   In fact   a·(1/a)=10,   which would contradict the rules of sign [O5] if we had   1/a0.
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