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[parent] positive (Definition)

The word positive is usually explained to mean that the number under consideration is greater than zero. Without the relation ``$>$ '', the positivity of (real) numbers may be defined specifying which numbers of a given number kind are positive, e.g. as follows.

For example, $1+1+1$ is a positive integer, $\frac{1+1}{1+1+1+1+1}$ is a positive rational and $5.15115111511115...$ is a positive real number.

If $a$ is positive and $a+b = 0$ , then the opposite number $b$ is negative.

The sets of positive integers, positive rationals, positive (real) algebraic numbers and positive reals are closed under addition and multiplication, so also the set of positive even numbers.




"positive" is owned by pahio.
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Other names:  greater than zero
Also defines:  negative

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Cross-references: even numbers, multiplication, closed under, algebraic numbers, opposite number, infinite, equivalent, decimal point, digits, natural numbers, decimal expansions, sequences, equivalence classes, real numbers, division, rationals, addition, integers, relation, number
There are 967 references to this entry.

This is version 16 of positive, born on 2004-09-06, modified 2007-06-06.
Object id is 6147, canonical name is Positive.
Accessed 19664 times total.

Classification:
AMS MSC00A05 (General :: General and miscellaneous specific topics :: General mathematics)
 11B99 (Number theory :: Sequences and sets :: Miscellaneous)
 06F25 (Order, lattices, ordered algebraic structures :: Ordered structures :: Ordered rings, algebras, modules)

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Discussion
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stretchy letters by MathNerd on 2007-08-13 17:04:55
The variables in this entry look all stretchy, I don't know why.

Also, I'm wondering about the thebibliography thing. After "begin{thebibiliography}" there is a "{1}" or a "{5}" or "{2}." I've never seen "{3}" or "{8}" for some reason. What do these numbers mean?
[ reply | up ]
proof by PARASHAR on 2007-03-26 00:20:57
prove that

sum(a:1->n)a^b/sum(a:1->n)a

is an integer (b is odd)
[ reply | up ]
  • Re: proof by TsurBaba on 2007-03-26 03:48:38
  • Re: proof by TsurBaba on 2007-03-26 04:10:08
    • Re: proof by PARASHAR on 2007-03-26 05:07:28
      • Re: proof by TsurBaba on 2007-03-27 03:53:22
        • Re: proof by PARASHAR on 2007-03-27 04:23:22
          • Re: proof by PARASHAR on 2007-03-27 05:11:35

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