To understand this, let us assume to have synthesized the compound in question via stereoselective synthesis starting with an achiral precursor. Then the enantiomer ratio is

[R]/[S] = exp(G / RT) = exp((GS  - GR )/RT)

where G_S  > G_R  are the free enthalpies of activation for the formation of the minor enantiomer S and the major enantiomer R (the "activation barriers"), R is the gas constant and T the absolute temperature of the reaction mixture. The enantiomer ratio is infinite only if the energy difference in the numerator of the exponent is infinite, or if T in its numerator is zero. Since G_S  and G_R  are both finite quantities, their difference cannot be infinite, nor can the temperature be zero.

If the compond sample at issue was obtained by separation of a racemate or by further enrichment of an already nonracemic sample, e.g. by chromatography on a "chiral column", then quite analogous considerations apply to the separation process. The important energy then is the difference of the free enthalpies of adsorption of the enantiomers at the chiral column material, both finite quantities, so that again their difference cannot be infinite.

Analogous considerations are valid not only for enantiopurity but even for chemical purity of a compound sample. The ratio of substance to impurity always exponentially depends on the difference of two finite energies, so that it can never be infinite. From this it follows: A completely pure compound sample does not exist.

And this is not the consequence of some missing accuracy of measurement, but the consequence of a fundamental principle.