Why Numbers Are Sets Export

@article{citeulike:147943, abstract = { I follow standard mathematical practice and theory to argue that the natural numbers are the finite von Neumann ordinals. I present the reasons standardly given for identifying the natural numbers with the finite von Neumann's (e.g., recursiveness; well-ordering principles; continuity at transfinite limits; minimality; and identification of n with the set of all numbers less than n). I give a detailed mathematical demonstration that 0 is { } and for every natural number n, n is the set of all natural numbers less than n. Natural numbers are sets. They are the finite von Neumann ordinals.}, author = {Steinhart, E.}, citeulike-article-id = {147943}, citeulike-linkout-0 = {http://www.ingentaconnect.com/content/klu/synt/2002/00000133/00000003/00406266}, issn = {0039-7857}, journal = {Synthese}, keywords = {benacerraf, philosophy\_of\_mathematics}, month = {December}, number = {3}, pages = {343--361}, posted-at = {2005-04-03 07:11:27}, priority = {3}, title = {Why Numbers Are Sets}, url = {http://www.ingentaconnect.com/content/klu/synt/2002/00000133/00000003/00406266}, volume = {133}, year = {2002} }

TY - JOUR ID - citeulike:147943 L3 - citeulike-article-id:147943 N2 - I follow standard mathematical practice and theory to argue that the natural numbers are the finite von Neumann ordinals. I present the reasons standardly given for identifying the natural numbers with the finite von Neumann's (e.g., recursiveness; well-ordering principles; continuity at transfinite limits; minimality; and identification of n with the set of all numbers less than n). I give a detailed mathematical demonstration that 0 is { } and for every natural number n, n is the set of all natural numbers less than n. Natural numbers are sets. They are the finite von Neumann ordinals. IS - 3 JF - Synthese SN - 0039-7857 EP - 361 TI - Why Numbers Are Sets VL - 133 SP - 343 KW - benacerraf KW - philosophy_of_mathematics AU - Steinhart, E PY - 2002/12// UR - http://www.ingentaconnect.com/content/klu/synt/2002/00000133/00000003/00406266 ER -