# What is the relationship between subsets of real number system

### The set of real numbers is a subset of the set of complex numbers? - Mathematics Stack Exchange The real number line and relations. One-dimensional coordinate system This means that the set of natural numbers is a subset of integers, i.e., N is a subset Z. The real number line is an infinite line on which points are taken to represent. Whole nubmers is branched to natural numbers and integers. I'm not sure that she has that right. The terms with which she is working include Real numbers, Surds, Opposites of number systems is a nice way to show their relations - in particular, noting which sets of numbers are subsets of other numbers. Subject: Subsets of the Real Number System. I am trying to help a new African student who speaks more French than English in a monolingual English school.

An outdoor thermometer may only show the subset of temperatures from minus 40 to plus degrees Fahrenheit. Working with subsets like these is useful because any result outside the expected subset is probably wrong. Sciencing Video Vault The more general subsets of real numbers classify numbers according to their characteristics, and these subsets have unique properties as a result. The real number system evolved from subsets such as the natural numbers, which are used for counting, and such subsets form the basis for an understanding of algebra. Rational numbers are integers and numbers that can be expressed as a fraction.

All other real numbers are irrational, and they include numbers such as the square root of 2 and the number pi. Because irrational numbers are defined as a subset of real numbers, all irrational numbers must be real numbers. Rational numbers can be divided into additional subsets. The natural numbers are numbers that were historically used in counting, and they are the sequence 1, 2, 3, etc. Whole numbers are the natural numbers plus zero.

Integers are the whole numbers plus the negative natural numbers. Other subsets of the rational numbers include such concepts as even, odd, prime and perfect numbers. Even numbers are integers that have 2 as a factor; odd numbers are all the other integers. Prime numbers are integers that have only themselves and 1 as factors. Perfect numbers are integers whose factors add up to the number. The smallest perfect number is 6 and its factors, 1, 2 and 3 add up to 6. My daughter is doing a tree diagram using terms related to math "numbers" for a calculus assignment.

Could you please explain in lay terms what surds are? I don't remember ever having that term, and she can't find it in her resources. She has the branch with irrational numbers completed; we're working through the rational numbers. She has one branch off rational numbers started - whole numbers. Whole nubmers is branched to natural numbers and integers. I'm not sure that she has that right. The terms with which she is working include Real numbers, Surds, Opposites of natural numbers, Even numbers, Repeating decimals, Non integers, Natural numbers, Irrational numbers, Transcendental numbers, Integers, Zero, Rational numers, Whole numbers, Odd numbers, Terminating decimals.

### Eighth Grade / Relationships Between Sets of Numbers

Thanks, Rina Hallock Date: Making a tree diagram of the various number systems is a nice way to show their relations - in particular, noting which sets of numbers are subsets of other numbers. For example, the natural numbers also called "counting numbers are a subset of the whole numbers. There is no subset of largest numbers. The list that your daughter's teacher gave her includes several redundancies. For example, you asked about "surds". A surd is another name for an irrational number.

## For Parents

Thus, sqrt 2 is a surd. It is also an irrational number. This means that when you try to evaluate it as a decimal, it neither repeats nor terminates.

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