What did georg cantor contribute to math?

Answer 1

· Cantor was the first mathematician to put a firm logical foundation for the term "infinity," and described a way to do arithmetic with infinite quantities useful to mathematics. He stated that a collection is infinite, if some of its parts are as big as the whole. Cantor also was able to demonstrate that there are different sizes of infinity.

· Cantor revolutionized the foundation of mathematics with set theory.

o One to One Correspondence: He showed that you could make a one-to-one correspondence between the natural numbers

§ (1, 2, 3, 4, ... } and the integers (..., -3, -2, -1, 0, 1, 2, 3 ...}

o Continuum Hypothesis: The cardinality of the set of all subsets of any set is strictly greater than the cardinality of the set

o For any set A, cardinality(powerset(A))>carinality(A)

· Transfinite numbers

o Used to count the number of integers and the number of real numbers