Tuesday, February 18, 2014

Getting mathematical - Understanding negative numbers intuitively

Hello there!

This is a second part of the series - "Getting Mathematical".Here I will be sharing some fun facts about negative numbers.

Question that we would try to answer is the following:

With positive numbers used to measure tangible things - what we can touch or hold (six cars etc.). What do we possibly mean when we flip the sign of a natural number? Intuitively.

What could -3 possibly mean? Or what could 10-12 mean? We can not say -2 apples. Then?

The answer lies in recognizing that apart from being used as a means of measurement, numbers can also represents concepts/relationships in the real world. While natural numbers are used for counting, negative numbers are more for capturing concepts like debt or comparisons [1]. So, in the question above, 10-12 can be used to model a situation where you have 10 apples but your friends needs a dozen. So, you are short of two apples. 

Another example: Negative numbers are helpful in modeling alternating patterns[1]. Consider a number x. If you keep multiplying it by -1, you will get the pattern x,-x,x,-x..The reason that we are considering multiplication by -1 is because it does not change the size of the number. So, allows us to focus on the concept of negativity.

Considering that the weather forecast of the day during a month is oscillating between rainy/sunny. Then knowing today's weather, you can ascertain the weather 20 days ahead without counting - rainy, sunny, rainy, sunny.....

Leveraging negative numbers back and forth behavior: we can say (rainy) * (-1)(power 20)= rainy.


That's pretty much about it for this post. I would appreciate if you write back! - questions/suggestions/comments?



[1] "A Visual, Intuitive Gide to Imaginary Numbers", betterexplained.com, K. Azad.
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