Infinite Sets

Ninibeth Palencia Magana and Dr. Ivona Grzegorczyk

Abstract

I will research first, and second-year students who are taking Math 230 Logic and mathematics, which is the Introduction to deductive logic, logical and critical thinking, and symbolic approaches to common language. Includes abstract sets and number sets, relations, propositional logic, and the theory of quantification. My main focus will be Infinite sets. Define infinite sets. We will study what the students have an idea of infinite sets by handing out a survey at the beginning and towards the end of the semester. A senior colloquium class will also take the survey. The survey will be a collective of four questions.
When are two sets equal?
Give an example of two sets, A and B, such that A is a proper subset of B, but they have the same number of elements.
Anna has set A={all natural numbers divided by 2}
Bob has a set B={all decimals}
Chris has a set B={all even numbers}
Do these sets include each other? How?
Do they have the same number of elements?
Let the infinite set L be the set of points(a,b) on the plane such that a,b are both natural numbers. Can you make an infinite list of all points in set L? Explain how.
I will count each question answered as 1:1 correspondence. I will be using graphs to show their growth and compare it to the senior colloquium class. At the end of the research, my goal is to understand what a first and second-year student might know about infinite sets and what they know about infinite sets at the end of the course.

One Comment

  1. Congratulations Ninibeth!

    The research is interesting — why do you compare younger students to more senior students? Since there is a much smaller size of students who responded at the end, how does that change the analysis of your results?

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