Number Sets, Positive and Negative Numbers and Number Lines

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1.2Number Sets, Positive and Negative Numbers and Number Lines


In these revision notes for Number Sets, Positive and Negative Numbers and Number Lines, we cover the following key points:

  • What is the definition of a set in general? What is a number set?
  • What are natural numbers? What common feature do they share?
  • What are whole numbers? Where do they differ from natural numbers?
  • What are integers? Do they have a beginning/end?
  • What are rational numbers? What is the name we more commonly refer to them as?
  • What are irrational numbers? Do they have anything in common with rational numbers?
  • How do we know whether a given number is rational or irrational?
  • What are real numbers?
  • What is a number line? In what direction do values increase in a number line?

Number Sets, Positive and Negative Numbers and Number Lines Revision Notes

Sets are groups or collections of items which have common properties.

The common feature all number sets share is that all of them contain not just numbers, but these numbers are related between them through a formula or rule.

Depending on the situation involved, we have the following sets of numbers:

Natural Numbers, N. This is the oldest set of numbers that includes numbers like 1, 2, 3, 4, .... etc. We can write the set of natural numbers N in a list form like

N = {1, 2, 3, 4, 5, 6, 7, ....}

The common feature, in this case, is that natural numbers represent whole and positive values. Natural numbers have a beginning (the number 1) but no end; they can extend to infinity.

Whole Numbers, W are similar to natural numbers but also includes zero. This set also has a beginning (the number zero) and no end. Hence, when this new set is expressed in list form, it becomes

W = {0, 1, 2, 3, ....}

Integers, Z includes both positive and negative whole numbers and a zero. It has neither beginning, nor end. When expressed in list form, the set of integers is written as

Z = {...,-3, -2, -1, 0, 1, 2, 3, ....}

Rational Numbers, Q (i.e. numbers written as ratios) represent sets of numbers which usually represent part of the whole. They are otherwise known as fractions. The distinctive feature of rational numbers is that the numerator of fraction must be an integer while the denominator a natural number.

Irrational Numbers, I are those numbers that cannot be expressed as fractions. A number can either be rational or irrational but not both.

The set of Real numbers, R includes all the above sets. This set includes both the whole and not whole numbers.

Numbers can be shown in a number line where the number zero is taken as origin. Positive numbers are usually placed on the right of origin while negative numbers on its left.

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