I have a strong affinity for infinity.
Something about about the infinitude of numbers draws me in.
My initial research interests:
I think it is because of this "affinity for infinity" that I initially wanted to investigate students conceptions about the density about real number line. Yes, many students know that there are an infinite amount of numbers. But, what do they think infinity is? Is it an idea or a number? And, how do students conceptualize the infinite amount of rational numbers in-between any two rational (or real) numbers? Although I am researching negative integers now, I definitely see myself eventually researching students' conceptions or ideas about infinity.
Infinity will blow your mind:
Infinity also has a way of blowing your mind (much like the AT&T Commercial below). In fact, when discussing infinity you are GUARANTEED a mind-blowing experience. For example, the size of infinity (or cardinality) of the set of real numbers between any two real numbers is just as large or infinite as the set ALL of the real numbers. Yet, the size of infinity for the set of even numbers is NOT as large as the size of infinity of (for example) the amount of real numbers between 1/2 and 3/4.
WHOA. Mind blown.
If you are looking for something less mind-blowing and more "infinity" friendly, let me recommend one of my new favorite children's books. The main character, Uma, talks about what she think infinity means and eventually compares infinity to the love that she has for her grandmother. So precious! And, I adore the illustrations.
"Infinity and Me" by Kate Hosford