Accepting that some numbers are not real is hard. In math, the definition of a real number is any number that represents a quantity along a continuous line. Real numbers can be positive or negative.

So if a negative number is real, how could one actually possess -5 dollars? It is easy to imagine a fraction of those theoretical dollars. Half of five dollars is 2.50, but how does a NEGATIVE number actual exist? The very concept of negative numbers was not widely accepted by most people until the 1700s, which is a long time after even the more complex number systems were developed.

A negative number expresses a relationship. If you have -5 dollars in your bank account, it is acknowledging that you have $5 LESS than you need. That is the relationship. It is not just 5 less than zero, it is a deficit of 5 in relation to how much money you are supposed to have.

So, a negative number is a REAL number, even if it is not one you can hold in your hands.

So, here is the tricky part. Imaginary numbers DO exist. So why are they imaginary?

An imaginary number is one that when squared gives a negative result. How would this even happen? We will look at that at a later time…

Let’s get back to the real task at hand.

How do you start liking math if you don’t already?

- Figure out why you don’t like it! Is it because it is hard? Maybe you it hasn’t come naturally to you – YET.
- Try to change your mindset. If you have convinced yourself that you don’t like it, you will not like it.
- Start learning concepts instead of memorizing. Think of math as a system, not just a subject consisting regurgitation.
- Don’t skip steps or take shortcuts. You have more potential to mess up and not be able to figure out where you went wrong. If you show your work, it is much easier to find the error.
- Think of math as a puzzle or a riddle. You are either piecing things together, or figuring out how to take them apart.