>>11001707The definitions of "whole number" and "integer" that I learned during American high school education are exactly what is described in the OP's graphic. There, the phrase "whole number" was an arbritrary one to distinguish {0,1,2,...} from {1,2,...}, the latter being called natural numbers.
I think it's very sad that the "proper" mathematical community can't settle on two words/phrases to distinguish between these two unequal sets, once and for all. The "naive" definition that I learned in my American high school, of all places, would be perfectly satisfactory as an unambiguous shorthand-if only everyone would adopt it (or a similar schema), uniformly and once and for all. That way everyone could dispense with the bit of setup about exactly what set is meant.
I appreciate that historically, in serious texts, the "natural numbers" denotes {0,1,2,...}, contrary to the above usage. Fine. Then you should still have a univocal phrase for the set {1,2,...} It is routine to speak of one set to the exclusion of the other, depending on exactly what math/counting argument you're doing (do not say: they're isomorphic/equivalent/etc If this were really enough then you wouldn't need the aforementioned declarations at early stages in a given text). So, one name should be given to the one set, and another name should be given to the other set, The End, and then all prior mathematical documents can be referred to as having occurred before the historic standardization.
