In class we were asked to come up with a sentence that we thought best described the word number. After we had a few minutes to come up with one we were asked at our table to come up with one sentence we all could agree on. After that, each table wrote their sentence on the board. No two sentences were the same. After all of the different sentence were on the board we all realized that there are so many different elements that go into what a number is. One group’s sentence was something giving quantity to an object or itself. The second group’s sentence was a value that’s a distance from zero. The third group’s sentence was a symbol that represents and amount. The last group’s sentence was something that carries meaning to the size of the set.
So which sentence best describes a number? It was time to put these sentences to the test. What’s a better test then actually using real numbers to see if it holds true. We needed to pick different numbers to see if it holds true for all types so we picked 0, -2, 1/3, , infinity. There were two sentences the whole class found to be right, those being a value that’s a distance from zero and a symbol that represents an amount. We found the other two sentences were wrong because something giving quantity to an object or itself was confusing to people and felt that it might not work for infinity. Then for the other sentence that was something that carries meaning to the size of the set we said did not work for -2 because if we think about it someone cannot have negative two apples. So as we can see that everyone might have an opinion about what a number is but to see if it is really true or not we need to test it. Since there is no one true definition of a number and we can have multiple ones since so much goes into a number testing it is the only way.
When talking about numbers and infinity it gets kind of crazy. I say this because a lot of people know about and use numbers and infinity in everyday life, especially in math, but when trying to put a definition to the words or describe what it is we find it difficult. We know what they both do and act like but cannot pinpoint a specific definition for them. Doing this activity really opened my eyes to how something so big in our lives as math majors can conclude a wrong definition for something like numbers. Its a big concept but asking anyone else if they think math majors would know what a number was my guess is there response would be I sure hope so. These people might not know how complicated the number system can actually get. With doing this activity in my classroom I would love to incorporate something along these lines so students can see and understand how many different pieces of the math puzzles goes into something like numbers. This can open their eyes to how we need to test things to make sure a definition actually fits what we are talking about and just how there are things behind the scenes that we can explore. There are so many things we do in math just because we know we can such as why a negative times a negative is a positive. Being able to explain why and explore this with my class is a great way for them to think deeper and to be able to get the full picture.