Let us examine this situation more closely. Finite numbers possess value. Value could be said to directly correspond to the size of a number. Value implies measurement. Measurement, by definition, is the documentation of a number's size.
Measurement is the 'fencing in' of the value of a number.
All values that can be measured are therefore definable values. Infinity, because it is not finite, is not definable. That is, the classic definition of infinity is that it is a value that is so large, no effort should be put towards defining it. Large implies size. Large' is a word that applies to finite numbers.