Sum Of Floor Of Irrational Numbers

This video covers this fact with various examples.

Sum of floor of irrational numbers.

A simple example is adding sqrt 2 and sqrt 2 both of which are irrational and sum to give the rational number 0. Will the sum of a rational and an irrational number be a rational number. Or will it be an irrational number. And their sum gives us another rational number.

So let s say that this first rational number we can represent as the ratio of two integers a and b. Let s look at what makes a number rational or irrational. The same goes for products for two irrational numbers. In mathematics the irrational numbers are all the real numbers which are not rational numbers that is irrational numbers cannot be expressed as the ratio of two integers when the ratio of lengths of two line segments is an irrational number the line segments are also described as being incommensurable meaning that they share no measure in common that is there is no length the measure.

A rational number can be written as a ratio of two integers ie a simple fraction. Well let s express that as the ratio of two other integers m and n. The product of two irrational numbers is not always an irrational number. In division for all rationals of the form q 0 p q are integers two things can happen either the remainder becomes zero or never becomes zero.

Irrational means not rational. Let s call this irrational number let s just call this x. The sum of two irrational numbers can be rational and it can be irrational. Yes yes the sum of two irrational numbers can be rational.

Or could it be either. To learn more about irra. So let s assume that this is going to give us a rational number.