Weekly Report & Reflection Week #5!

Reflection 5-

 The Mystery of Zero

The title of my reflection blog is 'Zero' today because that came up a lot in this week's session. What is the number zero? When you are a kid you learn that you cannot divide by the number zero. As we grow older we start to learn something different, we get the hint that if we divide by the number zero a lot of 'crazy' things happen. Today in class we were told that these things are against the laws of nature that we are so used to. So that's why we stay away from dividing by zero. 

But why?  Have you ever thought exactly why you cannot? I searched up to find some answers and I found this one by Dr. Tom:

"Because there's just no sensible way to define it.

For example, we could say that 1/0 = 5. But there's a rule in arithmetic that a(b/a) = b, and if 1/0 = 5, 0(1/0) = 0*5 = 0 doesn't work, so you could never use the rule. If you changed every rule to specifically say that it doesn't work for zero in the denominator, what's the point of making 1/0 = 5 in the first place? You can't use any rules on it.

But maybe you're thinking of saying that 1/0 = infinity. Well then, what's "infinity"? How does it work in all the other equations?

Does infinity - infinity = 0?
Does 1 + infinity = infinity?

If so, the associative rule doesn't work, since (a+b)+c = a+(b+c) will not always work:
1 + (infinity - infinity) = 1 + 0 = 1, but
(1 + infinity) - infinity = infinity - infinity = 0.

You can try to make up a good set of rules, but it always leads to nonsense, so to avoid all the trouble we just say that it doesn't make sense to divide by zero.

What happens if you add apples to oranges? It just doesn't make sense, so the easiest thing is just to say that it doesn't make sense, or, as a mathematician would say, "it is undefined."
Maybe that's the best way to look at it. When, in mathematics, you see a statement like "operation XYZ is undefined", you should translate it in your head to "operation XYZ doesn't make sense.""

You can find the above information and more from this website:
http://mathforum.org/dr.math/faq/faq.divideby0.html

You might also want to check this video out for more information:

That being said, let me briefly cover what we did today in class. We were introduced to the topics of integers and exponents. I learned that exponent is just a way to represent a given equation in order to shorten and simplify it. For example it is better to write 12^200 rather than to write 12 multiplying by itself 200 times. A lot more convenient.

In every class I learn something. This class I learned that sometimes to simplify math concepts you as a teacher have to 'lie'. For example, you have to say you can't divide by zero but in some dimensions of different mathematics you can. I also learned that we should watch out what we are saying as a teacher. For example it would be good to avoid saying "this is really easy" when in fact it is not easy. Not every student finds what you find easy is easy.