Here’s my thought process. Numbers are infinite, and decimals are infinite. Therefore units of measure are therefore infinite. A ruler may not be 1 foot long, it may be 1 + ( 1 × 10^-63836275783837472827263728) feet long.
To me, for a measurement to be exact, it has to be to the point where as you get to smaller and smaller decimals of the measurement, you get to the point where the additional decimals are infinitely 0. But if numbers are infinite, than the ability to continuously shrink down and get those decimals is infinite too. Doesn’t that mean it’s impossible to get these measurements?
And if these measurements are physically impossible to find, since the requirements for them are physically impossible to occur, doesn’t that mean that no object in the world has a physical set size? And moreso, that the space in between any two objects, as well as the size of those objects, are both by definition infinite?
In: Physics
>And moreso, that the space in between any two objects, as well as the size of those objects, are both by definition infinite?
This isn’t the case, for an easy example consider the numbers 0 and 1, the difference between them is just 1. There are an infinite number of real numbers between them, but there is still a finite ‘distance’.
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