There isn’t enough matter in the universe to represent the infinite number of decimal places required to correspond to an infinitesimal numerical value via a potentially infinite number of divisions.
In fact, even if there were an infinite (hypothetically) amount of matter and you kept adding “0” after the decimal point indefinitely, in the hope of one day adding a “1”, then doing so would simply result in a finite value – but if you don’t, you’ll never produce any value other than “0”.
Moreover, to claim something is infinitely divisible, i.e., potentially infinitesimal, is to assert the following:
Counting Paradox: It isn’t possible to divide something an infinite number of times (Assertion 1 above) – dividing a numerical value continuously and never stopping, will always result in a finite number of divisions.
Changed your mind? Instead let’s assume that, although we acknowledge it is impossible to count down to an infinitesimal numerical value… an infinite number of divisions do actually already exist – imagine perforated divisions yet to be parted.
Proceeding on the basis that an infinite number of divisions already exist, regardless of us creating those divisions, in a sense, is similar to what we do anyway, e.g., 1 / 10 = 0.1... we accept that 10 divisions ("ten-ness") exist even though we don’t actually have 10 numbers (or things) in front of us.
Numerical platonic beliefs are simply claiming values exist as abstract objects, i.e., have no physical form – and of course they don’t escape the logical numerical arguments presented against the existence of infinitesimal values, i.e., platonic numbers must still be numbers – meaning they must correspond to divisibility, addition, and exist as a continuing sequence.
Therefore, the platonical examples below apply equally well to real life supposed infinitesimal values.
Continuity Paradox: A platonic existence of numbers means there must already exist a completed sequence of numbers – it is impossible for a continuation of descending numbers to exist that continues from any finite value to an infinitesimal value (Assertion 2 above), i.e., descending numbers in the sequence will simply be half the value of their original (divided) number.
Simultaneous Paradox: A platonic existence also means there must already exist a numerical value, that after being divided by two, results in a value which is simultaneously: 1) Above 0 (i.e., to exist)... and 2) Equal to 0 (i.e., to not be divisible).
The above paradoxes apply to:
Likewise, a potentially infinite platonic existence means there must already exist some value that cannot be added to. This is also paradoxical, i.e., ultimately the same (equivalent) misconception as exists for “infinitesimal values” – both ideas having been translated from human minds, via words, into their definition.
In summary, dividing a value that is greater than 0 only ever results in finite values; likewise, adding to a value greater than or equal to 0 only ever results in a finite value – the only time a finite value becomes not! finite (finite's opposite) is when it doesn’t exist – hence, “infinite” (which includes infinitesimal) values simply don’t exist.