Real numbers are those which can be represented on a number line. As per definition , we should be able to plot numbers like √2, 0.333333…. , π etc. on the number line, but if we don’t know their exact precise value then how can we plot it?
I have seen couple of answers on Google where people have used a right angled isosceles triangle with base and altitude of 1 , and with the help of a compass and ruler they plotted it , but still it isn’t the precise value, right?
Or for 0.333…. , they divided the length of 1 unit in 3 equal parts and marked the length of first part as 1/3=0.333…. ; 0.3333….. is not a precise value then how can it be accurately plotted on number line ?
In: 0
> Real numbers are those which can be represented on a number line. As per definition
That isn’t really the *definition* of real numbers – it’s just a way of thinking about them. Real numbers are usually defined in terms of sets or sequences of rational numbers (fractions) – you can google “Dedekind cut” or “Cauchy sequence” if you want the full details, but they’re maybe a bit beyond ELI5.
> but if we don’t know their exact precise value then how can we plot it?
On a real-life number line, we don’t really know the *exact* position of any number, since we don’t have any perfect measuring devices. We can use real numbers to model reality in approximate terms, but they don’t correspond exactly to reality. For example, we know that there are infinitely many real numbers between 0 and 1, but are there are infinitely many points between two distinct positions in space? Nobody really knows.
Latest Answers