Definition:Infinite/Also known as

Infinite: Also known as

When Georg Cantor did his original work on his development of set theory, the concepts were considered alien and difficult to accept.

To sweeten the pill slightly, he coined the word transfinite, which he used instead of infinite, so as not to scare mathematicians who already had a conception of the meaning of infinite, and were having difficulty accepting the challenge to their notions.

Hence the concept of a transfinite set, which is exactly the same as an infinite set.

Contemporary mathematics does not bother much with the term transfinite, except inasmuch as it applies to the concept of a transfinite ordinal.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Cantor's theory of sets
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): transfinite number or set
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Cantor's theory of sets
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): transfinite number or set