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How does comparing numbers help to order numbers?
A "total order" of a set requires certain properties of the ordering function. For any A, B and C: Transitivity: A>B and B>C implies A>C Trichotomy: A>B or B>A or A=B These properties are true of the '>' operator meaning "greater than" when used to compare real numbers. This means that real numbers can be put in order by comparing them in pairs to see which is greater. Side note: without "Trichotomy", we would have a "partial order", where the order of the set would not be unique. For example, if the set were people, and '>' meant "is an ancestor of", then Transitivity would still be true, but Trichotomy would not. And there would be many ways to order a group of people so that descendants always came before ancestors.
Can a square of real number is a real number?
The square of a real number is always a real number.
Is zero a real number?
Yes, zero is a real number. It is not a counting number, but it is an integer, a rational number, and a real number.
Can a number with a square root be a real number?
Of course, not only can it be a real number but it is a real number. When you take the square root times itself, the result is a number that is real.
Are there real number that are not rational number?
A real number dosen't have to be a rational number as a real number can be rational or irrational i.e the root of 2 is irrational and real. So is (pi).
