Positive Real Numbers

 In mathematics, the real numbers include both rational numbers, such as 24 and 32/154, and irrational numbers, such as pi and the square root of two; or, a real number can be given by an infinite decimal representation, such as 7.66758768..., where the digits continue in a number of way or the real numbers may be consideration of as points on an infinitely long number line. (Source Wikipedia).

 

Properties of Real numbers:

 

Here we learn about the properties of positive real numbers :

If we add two real numbers that have the same sign, the result obtained will be a positive number.

In general, (positive number) + (positive number) = (positive number).

If we add two real numbers that have the different sign, the result obtained will be a negative number.

In general, (negative number) + (negative number) = (negative number).

The real numbers are structured by the well-known correlation “<” (less than). 

¨ r < v means there is a positive real number t such that  r + t = s. 

                "r > v means that v < r".

“r ≤ v means that whichever r <  s    or   r  =  v.  Fine point:  This means that both the statements “55 ≤55” and “45 ≤98” are correct 

 ”v ≥ r means that r ≤ v".

A real number r is whichever greater than 0 then it is positive, if equal to 0, or less than 0 then it is negative. As in the place of numbers, a few editors declare that r is positive if r ≥ 0.

If r and v are individual real numbers, then either r > v or r < v.  This means the numbers are in completely ordered. 

If r < v, the closed interval [r,v] is the set { x | r ≤ x ≤ v } and  the open interval (r,v) is the set { r | r < x < v }. 

 

Example problems

 

1)Example for positive real numbers in addition:

Addition of 8.1 + 7.1= 8.1 (+) 7.1 = 15.2
Here, the sum of the values are 15.2 and their sign as same as positive (+) so answer is = 15.2.

2)Example for positive real numbers in subtraction:

Subtraction in 8.2 - (3.2)
                       8.2 - (3.2) = 5.0
Here the subtraction value is 5.0

3)Example for positive real numbers in multiplication: 

Multiply -6.6 * - 6.6
                     -6.6 * -6.6 = (-1)(-1)43.56

                                    = + 43.56
the answer is 43.56