Welcome to the Mathematics Teachers' Circle of Austin!

This is the official site for the Mathematics Teachers' Circle of Austin. This professional learning community brings together middle and high school math teachers and professional mathematicians to work together and learn from each other.

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Fall 2025 MTCA Workshop #2

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.

Thursday, October 30, 2025
6-8 pm
PMA 12.166

Please visit our Previous Workshops page for information and handouts from previous sessions.

Information and handouts from previous workshops can be found by clicking on the Previous Workshops tab in the sidebar. There you will find links to all previous MTCA workshops. When handouts are available, they will be found as links at the bottom of each post. You can also find links to handouts from our summer workshops by clicking on Workshops, then following the links to the summer workshops.

Registration is free and open to all math teachers/instructional specialists/coordinators in the Austin area. Join us for dinner and problem-solving fun! See calendar below for more details.