Next 4 videos are a continuation of the last post, in here we will learn some more properties related to the absolute value of real numbers. In the first video we will study the concept of Triangular Inequality.

Property 7 and 8 relate the inequality behavior when two real numbers are added or subtracted.
Namely, ||a|-|b||< |a-b| and |a-b|< |a|+|b|. we will check how this happens.
In the last video we will prove why the property that says |x-1|<|x| holds true for all real numbers x. Continue reading →

In the next few videos we will work in detail on the concept of absolute value or modulus of real numbers. In the first video we will define it with examples and then further we will look at the properties related to modulus that are true for all real numbers.

In the second video we will understand the property that says |a.b|=|a||b| and that this holds true for all real numbers.

In the third video we will proof why |a|^2 is equal to a^2 in all circumstances, even when a is negative. In the fourth video we will proof two properties, property 3 and 4.

Property 3 shows how we can interpret modulus in terms of an interval and in property 4 we will learn that the real number a lies between the positive and negative values of the absolute value of a. Continue reading →