Cantor's construction starts with the set of transcendentals T and removes a countable subset {tn} (for example, tn=e/n). Call this set T0. Then T= T0∪{tn}= T0∪{t2n-1}∪{t2n}. The set of reals R= T∪{an}= T0∪{tn}∪{an} where an is the sequence of real algebraic numbers. So both T and R are the union of three pairwise disjoint sets: T0 and two countable sets. A one-to-one correspondence between T and R is given by the function: f(t)=t if t∈T0, f(t2n-1)=tn, and f(t2n)=an. Cantor actually applies his construction to the irrationals rather than the transcendentals, but he knew that it applies to any set formed by removing countably many numbers from the set of reals (Cantor 1879, p.4). Georg Cantor (1879). «Ueber unendliche, lineare Punktmannichfaltigkeiten (1)». Mathematische Annalen. 15 (1): 1–7. doi:10.1007/bf01444101
Cantor's construction starts with the set of transcendentals T and removes a countable subset {tn} (for example, tn=e/n). Call this set T0. Then T= T0∪{tn}= T0∪{t2n-1}∪{t2n}. The set of reals R= T∪{an}= T0∪{tn}∪{an} where an is the sequence of real algebraic numbers. So both T and R are the union of three pairwise disjoint sets: T0 and two countable sets. A one-to-one correspondence between T and R is given by the function: f(t)=t if t∈T0, f(t2n-1)=tn, and f(t2n)=an. Cantor actually applies his construction to the irrationals rather than the transcendentals, but he knew that it applies to any set formed by removing countably many numbers from the set of reals (Cantor 1879, p.4). Georg Cantor (1879). «Ueber unendliche, lineare Punktmannichfaltigkeiten (1)». Mathematische Annalen. 15 (1): 1–7. doi:10.1007/bf01444101
Bruno, Leonard C.; Baker, Lawrence W. (1999). Math and mathematicians: the history of math discoveries around the world. Detroit, Mich.: U X L. p.54. ISBN0787638137. OCLC41497065
