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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.
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What is comparing and ordering rational numbers?
Rational numbers are roots, decimals, fractions, and whole numbers. Bascially anything that can become a decimal. Irrational numbers are like pi. I'm pretty sure to be irrational, they have to repeat. Anyway, ordering them and comparing them means looking at them and seeing which is smallest and largest. Then you order them (smallest to largest or whatever it says).
How does a number line help compare numbers?
order the numbers from least to greatest
How does knowing how to compare four digit numbers help you to compare five digit numbers?
they all are digit numbers
What are two methods for comparing numbers?
ratio and difference
How is comparing mixed numbers and whole numbers different?
Mixed numbers have fractional parts that must be compared; whole numbers do not.
