But look at at the plain meaning of the word: "infinite" is "in finite". More seriously, if you aren't careful in your interpretations, you observe that the re

But look at at the plain meaning of the word: "infinite" is "in finite". More seriously, if you aren't careful in your interpretations, you observe that the real interval [0,1] has finite measure but infinite cardinality. And the rational interval has 0 measure but infinite cardinality, so you do find infinite in the finite.