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While reading some articles, I got a bit confused by the definitions of numbers. Specifically,

  • Can the number line contain decimal values?

    I read that Real numbers = All numbers on the number line.
    My understanding was ..,-3,-2,-1,0,1,2,3,.. made up the number line.

If so, is it that the set of Real numbers can only be the negative integers, 0 and positive integers? That doesn't seem right.

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"The number line" typically refers to all real numbers. Integers ("whole numbers") are a subset of all real numbers. –  Eric J. Apr 4 '12 at 5:01
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2 Answers

up vote 2 down vote accepted

Real numbers = All numbers on the number line

Yes and this doesn't mean that real numbers = all numbers usually written down this line, but all numbers that could be represented as a point on this line.

My understanding was ..,-3,-2,-1,0,1,2,3,.. made up the number line.

That numbers are only the points on the number line.

UPDATE:

Representations of a number line may vary.

enter image description here

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Number line also container decimal numbers like 1.5 and more .... which basically depends on the level of depth you want to represent the number line too.

There is no such notion that decimals can't be represented on number line.

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