Surreal numbers also extend real numbers to a system which satisfies the axioms of an ordered field, and so addition behaves similarly to hyperreals, in that x < x + 1 for all surreals x. In this system, one may find elements corresponding to infinite ordinals; however, surreal addition and multiplication correspond not to the usual ordinal operations, but to the natural sum and natural product.
Infinity plus one is a phrase used in relation to the notion of infinity as the largest possible amount. 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: