Political Algebra

It's no surprise to anyone that in this day and age, school subjects have become as politicized as anything else. Social sciences were among the first to go. History is taught with a vicious slant. It's now worming it's way into the harder sciences, as the PC crowd is looking to put quotas in "STEM" fields (note to self: invest in "classic" tech). It's only a matter of time before mathematics, the only pure bastion of reason, falls. I can't win, I realize that now. There is nothing to do but try to get ahead of the curve.

We'll begin with some classic, or "conservative" algebra."

For variables X and Y, where X does not equal (≠) Y,

X + Y = Y + X, and XY + XX = XX + XY

XY = YX,   However XY ≠ XX ≠ YY (Whatever that is)

Honestly, a lot of people never master Algebra, and that's fine, but most people throughout history have managed to handle these concepts. You could almost refer to them as defining, natural laws for all societies, at least those that lasted for any length of time. Recently, however, there has been a shift in the wind, and the old ways aren't good enough for anything. So now, according to "Liberal" Algebra:

For variables X and Y, where X does not equal (≠) Y, (≠) is considered an arbitrary construction. So in fact, there may be cases where, 

XY = XX =YY (Whatever that is)

 On the other hand, should it desire to be so, XX may be greater than XY. XY may be considered less than XY, but only in a particular aspect, and not in such a way that is deemed to lower it's relative value overall to XX.  (It should be noted here that in Conservative Algebra, XX and XY are considered separate but equal complements of a set.) 

Now, should XY desire to increase it's absolute value, it may adopt XX characteristics, keeping in mind that it's relative value may approach, but not exceed, XY. Some XX variables are generated with a tendency toward an XY alignment, which seems to result in an XY prime (XY') variable that may be commutative, is limitedly associative, but not independently multiplicative. Similarly, there is an XX' variant with equal and opposite tendencies and properties that appear to resist classical combination laws. 

The end result of this is, of course, that a once orderly system is rapidly degrading as systems built to handle classical programming attempt to ingest a series variable premises and contradictions. You can juggle the X's and the operations forever. Unless you come up with a good reason for Y, you'll never solve the problem.