MTH 495 – Blog Post 2

O Zero, Zero, wherefore art thou Zero?

Perhaps this is just another example of just how long it has been since I was in high school, my 25-year class reunion is this summer, but I do not remember a time in my life were I considered a life or a mathematics without the number zero in it until I started taking classes at GVSU. Since then, I have learned that zero was invented and the meaning of the number and the properties had to be developed. Whoo! What would life be like without zero!?

Well, before we get to that, how about we talk a little bit about what life is like with zero. Here is a link to a School House Rock video about zero (https://youtu.be/3huvvxUHDmM). Did you watch it? What do you think? Is there anything you disagree with or question? Certainly as a kid growing up and watching these videos during Saturday morning cartoons, I never questioned them. Yet now, I am not so sure about some of what the video says:

• What do they mean that without zero we could never reach a star?
• That implies a great deal, including that because we have zero, we can reach a start. Yet current experience has shown us that by the time anyone was to reach a star, actually it would be one of the ancestors of those that started out towards the start, they would have serious difficulties dealing with the effects of gravity, to say the least.
• What do they mean by, “Before you came along, we counted on our fingers and toes.”?
• I think that the Chinese, Egyptians, and Babylonians might disagree with that.
• Although, we have to be careful here because without zero, what would the cavemen shown in the video do when they got to the tenth finger or toe?
• The use of zero in this case seems to refer to using it as a place holder to indicate, for example, the difference between one and ten. Archeologists and historians have found numerous examples of the use of a variety of symbols used as a place holder. Other examples show that no place holder was used and the only way you could tell the difference between six and sixty for example, was by the context it was written in.
• “When you run out of digits, you can start all over again.”
• Actually, I am fascinated by math that does not use zero and what it does to the standard mathematical properties that we use every day. This is what I will look at in the next section.
• “Place a zero after any number and you have multiplied that number by ten.”
• I love the simplicity of that. Which is why the metric system is so nice and why it is surprising that the US still hasn’t switched to it.
• Also, it is surprising how many students don’t have a firm understand of this.
• Zero is definitely useful in our 10 based number system as a place holder but to me, the real power and beauty of zero comes from the properties it has as a number. In class we looked at the definitions of zero laid out by Brahmagupta around 630 AD. His definitions, or should I say properties, used the terms fortune and debt for positive and negative numbers. Interestingly, he had definitions for division by zero! Math teachers: It’s okay! You can come out from under your desk. Because of the conflicts these rules created, we have decided that division by zero is just not something we want to define quite yet.

So, now a brief look at math with and without the number zero. What I will do is set up a 9x9 grid for both addition and multiplication and see what the answers are using a number system that goes on to 10, 11, 12, … and one that wraps around to 1 again after you go past 9. I am interested in seeing what happens.

Okay, I am the first to agree, there is so much more to look at here and explore. We have really just scratch the surface. Please share your observations as a reply. Also, do you have anything to add, did I have an error or miss something? Please share!

Thank you for reading,

Jerry