The Athens Algebra Seminar presents “A quick introduction to the Hyperreals” by Javier Ronquillo of Ohio University on Thursday, Nov. 5, from 4:35-5:30 p.m. on Morton 218.
Abstract: We will use the machinery of ultrapowers to build the Hyperreal numbers. The nice thing about this construction is that we can use a Transfer Principle to prove statements about the real numbers by proving an equivalent statement in the hyperreals real numbers and vice versa. One of the things that is gained when proving statements in the hyperreals is that we get back the intuition about infinitesimals. Imagine all those proofs that we consider unrigorous because they used the concept of a quantity infinitely small that is not zero, the infinitesimals and hyperreals provide a formal and rigorous way of writing these proofs without losing the intuition. We will use this frame to prove many results such as the Fundamental Theorem of Calculus.
Comments