Day 5: Real Numbers

hello frndz,

today we will learn about real numbers and some of their properties.

:- Number Line: A number line has a center with value 0. Left side, it has negative numbers and Right side, it has positive numbers.

:- All numbers reside on number line are known as Real numbers. All real numbers except zero are either positive or negative.

:- If you say, A number n is between 1 and 4 then you will write 1<n<4 and if n is 'between 1 and 4, inclusive' then 1<=n<=4

:- Absolute value: the distance between a number and zero on the number line is called Absolute value.
For eg. 3 and -3 are either side of 0 but has same absolute value (i.e. 3).

(Easier definition: A distance that you have to travel from zero to reach at that number means to reach at both number 3 and -3, you have to travel 3 units from zero.)
Absolute value is a distance and distance can not be negative so absolute value always be positive.
Modulus value = absolute value
So |3| = 3 always;


:- Properties of real numbers: Let's take x,y and z as real numbers.

1. x + y = y + x and x*y = y*x
2. (x + y) + z = x + (y + z) and (xy)z = x(yz)
3. xy + xz = x (y + z)
4. If x and y are both positive, then x + y and xy are positive.
5. If x and y are both negative, then x + y is negative and xy is positive.
6. If x is positive and y is negative, then xy is negative.
7. If xy = 0, then x = 0 or y = 0.
8. |x + y| <= |x| + |y| (check it for all four condition i.e. x and y positive, x and y negative  and either is positive).


Okie guys, Keep practice on!!! Hope you are doing well.....



Er. Ankur Garg
garg.ankur6@gmail.com