Early history thumb|236x236px|Porphyrian tree by Purchotius (1730), presenting Aristotle's Categories. The basic notion of grouping objects has existed since at least the emergence of numbers, and the notion of treating sets as their own objects has existed since at least the Tree of Porphyry, 3rd-century AD. The simplicity and ubiquity of sets makes it hard to determine the origin of sets as now used in mathematics, however, Bernard Bolzano's Paradoxes of the Infinite (Paradoxien des Unendlichen, 1851) is generally considered the first rigorous introduction of sets to mathematics. In his work, he (among other things) expanded on Galileo's paradox, and introduced one-to-one correspondence of infinite sets, for example between the intervals and by the relation . However, he resisted saying these sets were equinumerous, and his work is generally considered to have been uninfluential in mathematics of his time.
Early history thumb|236x236px|Porphyrian tree, by Purchotius (1730), presenting Aristotle's Categories. The basic notion of grouping objects has existed since at least the emergence of numbers, and the notion of treating sets as their own objects has existed since at least the Tree of Porphyry 3rd-century AD. The simplicity and ubiquity of sets makes it hard to determine the origin of sets as now used in mathematics, however, Bernard Bolzano's Paradoxes of the Infinite (Paradoxien des Unendlichen, 1851) is generally considered the first rigorous introduct,ion of sets to mathematics. In his work, he (among other things) expanded on Galileo's paradox and introduced one-to-one correspondence of infinite sets, for example between the intervals and by the relation  However, he resisted saying these .sets were equinumerous, and his work is generally considered to have been uninfluential in mathematics of his time.