What is the difference between locating 3/5 on a number line and locating √5 on a number line?

Question

Jeffrey Reese

Mathematics

6 December, 00:20

What is the difference between locating 3/5 on a number line and locating √5 on a number line?

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Brock Bass · Answer 1

3/5 is 0.6 and is a rational number.

√5 however is an irrational number.

It would be quite easy to find 0.6 on a number line. It's only 6/10. It's made up of six tenths.

Now √5 is equal to 2.236067977 ... to infinitum.

It's made up of many little and random fractions; to a certain degree infinitely many little and random fractions.

This means that you'd never be able to find its precise value on a number line. You could zoom in to that line for eternity and never find the precise value of √5. You'd think you're getting closer to it's precise value - but it slips away and you just can't reach it.

... Welcome to the asymptotic realm of mathematics. You've been pixelated, digitized and spaghettified. Life will never be the same again.