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 ?
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Real numbers on a number line can (in theory) be plotted with as much precision as your number line.
If your number line has interval precision, then pi can be plotted somewhere between 3 and 4.
If your number line has n’th decimal place precision, then pi can be calculated to the n’th decimal and plotted.
An infinitely precise number line cannot exist in real life. Just how we can’t calculate pi to infinite digits.
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