# Two Plus Two Equals Four Until You Redefine Addition

Like everything else, the Babylon Bee had fun with this:

In a mathematics lesson delivered to her kindergarten class Tuesday, local teacher and closed-minded bigot Becky Delatorre reportedly insisted that two plus two equals four, all the time, to the exclusion of all other numbers, no matter how anyone feels about it.

Well…we turn to the famous Russian mathematician Israel Gelfand’s Lectures on Linear Algebra (Dover Books on Mathematics), who at the start makes this definition:

Breaking it down, in the italics he makes a definition of what a vector space is.  At the core of that definition is what linear algebra (which itself is at the core of numerical methods, computer simulations, etc.) is all about: everything that happens is basically scalar addition (which is what the kindergarten teacher in the Bee was trying to teacher her bratty students) and scalar multiplication, and lots of it for large models.

That definition made, Gelfand sets forth eight (8) rules for these two operations to follow in order to be valid.  At this point, Gelfand puts in the kicker:

It is not an oversight on our part that we have not specified how elements of $R$ are to be added or multiplied by numbers.  Any definitions of these operations are acceptable as long as the axioms listed above are satisfied.  Whenever this is the case we are dealing with an instance of a vector space.

What he is saying is this: for a valid vector space, we can redefine addition and multiplication as long as it meets the eight rules!  An example of how that works is here.

This is an interesting twist in mathematics that, mercifully, doesn’t have much practical application.  But I suppose it’s possible to shut up (or put to sleep, either result works) a class of unruly kindergartners with the eight rules.  And having endured stuff like this makes attacking Bill Clinton’s Eucharistic Theology even more fun.

Better stick with $2 + 2 = 4$