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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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Q: How does comparing numbers help to order numbers?

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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).

order the numbers from least to greatest

they all are digit numbers

ratio and difference

Mixed numbers have fractional parts that must be compared; whole numbers do not.

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There is no LCM of 144584 because in order to have an LCM there must be at least two numbers that you are comparing.

the operations that can be used in comparing two numbers are??????

it separating the whole numbers from the fraction parts.

-230 < -335, is it right?

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.

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).

ilgilili

<, ≤, >, ≥, and =

order the numbers from least to greatest

The comparing and ordering of numbers is referred to as factorization. Numbers are factored into certain multiples such that the resolution of the entity into the factors when multiplied together will give the original entity.

they all are digit numbers

they are the same because they both have whole numbers