The mole is a bridge between our world and the atomic world

The existence of Avogadro's number can also be used to discount "scientific" ideas that are a bit too interesting. The fact that Avogadro's number is a counting number - a number of things - implies that a finite number of atoms exist in a given amount of material. That is the basis for scientific criticism of homeopathy, in which medicinal materials are so thoroughly diluted that Avogadro's number would imply that not a molecule of the medicinal material remains!