Fall 2025 MTCA Workshop #2

Thursday, October 30, 2025

6-8 pm

PMA 12.166

Dr. Renee Cabrera

Taming Infinity

In this talk, we explore how mathematics tames infinity by distinguishing between its different sizes. We begin with familiar countable sets such as the natural numbers N, integers Z, and rational numbers Q, showing how each can be placed in one-to-one correspondence with N. Through short videos and visual demonstrations, we illustrate how these mappings work and why they matter. We then contrast these with the real numbers, R, which cannot be listed or matched with N, revealing a strictly larger, uncountable infinity through Cantor’s diagonal argument. Using one-to-one, onto, and "bijective" functions, we formalize the concept of cardinality and develop tools for comparing infinite sets. Participants engage with these ideas by constructing their own functions and exploring what makes a set countable or not. This approach blends visual intuition with mathematical rigor, offering an accessible path to understanding how infinity can be compared, measured, and classified.

We validate campus parking and provide dinner, and participants earn CPE hours (TEA approved) for this workshop.

Register by noon on 10/29 here.  

Free parking is provided in the Speedway Garage (SWG). Enter the garage on Speedway, between Dean Keaton and 27th street. Pull a ticket when you enter the garage. We will give participants cards to exit. (If the Speedway Garage is full or being used for an event, please park next door in the 27th Street Garage.)