If numbers are infinite, and they can get infinitely smaller, then how is it possible that we can touch anything? Wouldn’t the distance between my foot and the floor, for example, just keep getting infinitely smaller?
In: Mathematics
When two things “touch” we usually take this to mean that the distance between them is zero. In a mathematical sense, things can touch simply by having a portion of them occupy the same space. Moving things that start apart can approach each other and eventually touch. Issues you arise are solved through things like limits and calculus.
In the real world, things can’t touch in the mathematical sense because everything is made up of volume-less point-particles and physics says that two particles cannot occupy the same space (barring black holes).
In practice, we say that two things are touching in the real world when there is no noticeable space between them. Generally this becomes apparent when repelling forces between the electrons in the atoms in each object becomes noticeable (in the sense that you cannot bring the objects any closer and the friction between the two objects is noticeable).
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