In mathematics, infinity plus one is a concept which has a well-defined formal meaning in some number systems, and may refer to:
Transfinite numbers, numbers that are larger than all the finite numbers.
Cardinal numbers, representations of sizes (cardinalities) of abstract sets, which may be infinite.
Ordinal numbers, representations of order types of well-ordered sets, which may also be infinite.
Hyperreal numbers, an extension of the real number system that contains infinite and infinitesimal numbers.
Surreal numbers, another extension of the real numbers, contain the hyperreal and all the transfinite ordinal numbers.
This boils down to a variation of the Hilbert’s Hotel paradox, which we talked about way back in our very first post, Infinity plus one. ↩ Recall that we don’t allow letter combinations that would …
26 Jun 2018 · The word geodesic comes from “geo,” i.e., Earth, and “desy,” i.e., measuring, since you use great circles in order to measure distances on the Earth.↩
26 Jun 2018 · In the last couple of posts, we've talked about what math is (a search for what must be) and where the foundational axioms and definitions come from. Mathematics tries to prove …
24 Sep 2017 · The first post on the different sizes of infinities: Infinity plus one –> Next Post: The Cantor Set
25 Mar 2017 · Technically, a geodesic.We’ll get there eventually. ↩ In particular, it causes the parallel postulate of Euclid to fail. Euclid’s proof that the angles of a triangle add up to 180 …
29 Mei 2017 · The Schwarzschild spacetime is not the only spacetime with a black hole. It's just the simplest one. In fact, there are infinitely many possible types of black holes. Pretty much …
22 Apr 2017 · Special relativity, which we introduced a while ago, is a really good theory. The combining of time and space into a single manifold, spacetime, turns out to be really …
10 Nov 2017 · Though those stodgy engineers and accountants may disagree with me, one of the most exciting parts of mathematics is learning about a result so bizarre, so against your …
21 Jun 2017 · In the last post, we talked about what math is. To me, math is a quest of understanding what must be. The basis for this quest are the axioms and definitions of …
math is awesome. If you have ever traveled between the US and Europe, you may have wondered why your flight always seems to fly over Iceland.
