Infinity plus one

In mathematics, infinity plus one has meaning for the hyperreals, and also as the number ω+1 (omega plus one) in the ordinal numbers and surreal numbers. This phrase is also found in popular culture.

Mathematics

If "infinity" is interpreted as any specific transfinite cardinal number κ ≥ $\aleph_0$ in cardinal arithmetic, then "infinity plus 1" = κ+1 = κ.

Popular culture

Infinity plus one is a phrase used in relation to the notion of infinity as the largest possible number. The idea is that no such number should exist.

The phrase is also found in children's culture by those who have discovered the concept of infinity. When one child makes a reference to infinity, another may try to best them by making a similar reference to infinity plus one. One example of this is when children come up with a dare, and subsequently return the dare, multiplied by increasingly higher values, for example:

Child 1: "I dare you."

Child 2: "I double dare you."

Child 1: "I triple dare you."

Child 2: "I dare you times a million."

Child 1: "I dare you times infinity."

Child 2: "I dare you times infinity plus one."

This sort of exchange has been used in many popular television programs, such as The Simpsons, My Little Pony: Friendship Is Magic, Timon and Pumbaa.

One "Dilbert" strip showed a enemy of the title character promising Bob the Dinosaur "infinity plus two" times the wages Dilbert paid him.

See also

• Beyond the Infinite
• Eternity and a Day

References

• Monaghan, John (2001). "Young Peoples' Ideas of Infinity". Educational Studies in Mathematics 48 (2): 239–257. doi:10.1023/A:1016090925967. 
• Shulman, Polly (December 1995). "Infinity Plus One, and Other Surreal Numbers". Discover 16 (12). 
• Tall, David (2001). "A child thinking about infinity". Journal of Mathematical Behavior 20 (1): 7–19. doi:10.1016/S0732-3123(01)00058-X.