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If I would draw a right triangle with legs of length 1 centimeter with a ruler then its hypotenuse should be equal to $\sqrt2$ which is an irrational number - therefore its decimal representation, which is the limit of the sequence $\lim_{n \to\infty}\sum_{i=0}^\infty{\frac{a_i}{10^i}}$, has infinitely many numbers after the interger part of$ \sqrt2$.

What exactly can the ruler measure when drawing such a triangle, considering the fact that we draw irrational number (which by definition is infinitely long)?

I hope the question is clear.

Thanks.

  • 1
    Define *ruler*.2012-05-04
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    Also, consider how would you measure $1/3$ with a metric or imperial ruler.2012-05-04
  • 0
    Why do you insist to discuss a number, which cannot be described by a finite sum of digit-multiples of powers of ten in terms of "long"?2012-05-19
  • 0
    not long, infinitely long.2012-05-19

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