zero :(

[leonardo shawon]

im confused.. Amm, whats correct?
real number, R={0,1,2,3,4,5....}
or R={1,2,3,4,5. . . . }

[tanvirab]

I think you mean "Natural numbers".

Different people use different definitions. It does not really matter, as long as your are consistent in what you use.

I personally, use "positive numbers" or "non-negative numbers" to get rid of the ambiguity. This is the most common convention in modern mathematics.

[leonardo shawon]

thank u. But actually my question is, is Zero in Positive Real Number Set?

[leonardo shawon]

thanks 4 Natural Number:) i didnt know that.

[Moon]

Real number is not only integers (পূর্ণ সংখ্যা).They can be fractions, irrational numbers as well. In generals all the numbers on the real line is real numbers.
Zero is not a positive (or negative) real number. You can include zero with positive reals by considering the set of non negative reals. In the same way zero is in the set of non positive reals.

[leonardo shawon]

amm,, then, if f : R - R+
what will i do? Considering Zero as a non negative or Non positive..?

[tanvirab]

As Moon said, zero is not positive, not negative.

[leonardo shawon]

so,, where to put it??
First prove for a>0, then a=0 and then a<0 . . . . . . ?

[tanvirab]

Not sure what you mean.

Real numbers $> 0$ are positive
Real numbers $< 0$ are negative
$0$ is neither positive nor negative

[leonardo shawon]

okayy., thank uu:-)