I've been learning about negative numbers this quarter, and... I dunno, I think they're actually kind of fascinating in how they behave in an equation.
So... A negative number is basically a number that is smaller than zero, and a positive number is a number larger than zero. But... it also goes a lot deeper than that.
If you add a positive number and a negative number together (1+(-2)=-1), you basically get a subtraction that can be ordered however you want (though if you try to change the order of a normal subtraction equation, it makes a huge difference to the result).
But if you subtract two negative numbers (1-(-2)=3), its basically becomes a double negative and actually adds the 2nd number.
I also learned how algebra can be applied to graphing, and I think it's interesting how if an equation has an Absolute Value in it, it usually graphs into a V shape. I think this is because absolute value always turns a negative number into a positive number, which means that its output can never go below zero. So... basically what you get is a line graph that 'bounces off' of of a certain point of the Y-axis, and starts going back up again. In a simpler formula this lowest point would be zero, but if there's other things happening in the formula, this V can be moved around, and can even dip below Y-0.
I also realized that when you graph a formula using a calculator, the continuous line it shows you is basically a 'map' of every possible output of the function can produce.
...Math babble aside, I think it's kind of crazy to look back at when I was a teenager struggling to learn these concepts, and... past me never imagined I'd ever be talking like this about math. It feels like a miracle to have it make this much sense.
