## Friday, December 4, 2009

### Some are more equal than others

Some math concepts really aggravate people. One is the concept where we compare the members of a set to see if a member is greater than, equal to, or less than another member. Although this seems contrary to our democratic ideals that all are created equal - hey, it's math, not politics or human rights! Or science fiction.

Or e-commerce. There's actually a website called Equals.com that allows you to make Facebook party line calls - dial one number and get 5 people at a time. Wow! Of course, if you read the fine print, you learn that a subtle computerized voice will break into your conversation every five minutes with a sales pitch for something!

Before I give you the math sales pitch for equality or inequality, can I give you the signs?

> Greater than
>> Very much greater than
< Less than
<< Very much less than
≥ Greater than or equal to
≤ Less than or equal to
= Equal to
≠ Not equal to
≅ Approximately equal to; Congruent

I think those cover all the bases, value-wise. Bases, signs, pitch, get it? Ha ha ha. Maybe I should wait til baseball season starts to spring (training) these puns on you. OK, I know, don't quit my day job.

The symbol we use the most in math is the equals sign. It's been around for about 440 years. It was developed in England when its inventor, Doctor Robert Recorde, got tired of writing out longhand "such and such is equal to this" and "so and so is equal to that". He didn't get rich off this invention; in fact he died in prison a year later. But the symbol lives on.

Pretty soon we had a whole collection of shorthand symbols to save energy and ink.

These symbols are all related to one of the most important concepts in math - the notion of value. Does one value differ from another or is it the same? Here are some everyday examples:
• were you going faster than the speed limit?
• is this check going to be larger than the balance in my account?
• are there more people booked on this plane than there are seats?
• is it farther to the destination than we can drive on the fuel in this car?
• is this cup is holding less than or exactly 8 ounces of liquid?
Some of us were taught the alligator rule regarding the greater than/less than signs. Alligators are always hungry, so they are trying to eat the larger (greater value) number. Here he is:

There are lots of other ways that we use variations of these signs, especially in programming and logic. These are perhaps more closely related to identity than value, but I'll toss them in here anyway just for fun.

≡ Identical to
~ Roughly equivalent to
||  Incomparable to (you can't compare them)
<. Contained within ( Set A <. Set B means A is part of B)
<: A special type of ( Set A <: Set B means A is a subtype of B)

PS - my apologies if your browser does not render these symbols correctly