Do any of you have any suggestions as to where to begin on some of the more general language and form aspects of math, or could identify some of the best areas for me to study to begin to work with things such as the above? My formal background with mathematics has been to the level of calculus 3 and some basic differential equations. I've been pondering set theory and abstract algebra but I am hoping to work towards this type of content in the most efficient way possible and thought I would check with experts to see if I'm on the right path.
The first thing to note is that in algebra we use letters as well as numbers. But the letters represent numbers. We imitate the rules of arithmetic with letters, because we mean that the rule will be true for any numbers.
Here, for example, is the rule for adding fractions:
a + b
= a + b
The letters a and b mean Whatever numbers are in the numerators. The letter c means Whatever number is in the denominator. The rule means:
"Whatever those numbers are, add the numerators
and write their sum over the common denominator."
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