# What is an equation? | General Discussion Topics | Forum Guest
Search
Forum Scope

Match

Forum Options

Minimum search word length is 3 characters - maximum search word length is 84 characters  What is an equation? at1with0
Member
Forum Posts: 9244
Member Since:
April 9, 2009 Offline

I've been thinking, for whatever reason, what ET math would be like. I bet a lot of people would think that it and our math will not only be comparable, they will likely be essentially identical. For example, the induction principle in arithmetic would likely also be a theorem in their math. The Pythagorean theorem is probably among their theorems, as another example though their name for it (if it has a name) might be just "Theorem #691,865,863,532,987".

To that end, I was wondering how various ET mathematicians might define the word equation. A lot of us on earth are taught first off that an equation is just a formula or expression that contains the following symbol: =. But the ETs won't have that symbol in their language. So when fabricating the Rosetta Stone which will provide a means to translate their language to ours and vice versa, to give the proper meaning of our word equation, we have to capture the essence of what equality is.

Equality is a "principle" of sorts that exists only in certain formal systems. Many formal systems have nothing like equality while other formal systems have an equality. If xEy (which intuitively means x=y) is a grammatically-correct utterance in the formal system and if E is a symbol in the formal system possessing the following properties, then I would say E represents equality:
1. What E points to is an equivalence relation, meaning
1a. for all x, xEx (reflexivity)
1b. for all x and y, if xEy then yEx (symmetry)
1c. for all x, y and z, if xEy and yEz then xEz (transivity)
2. every equivalence class defined by E has cardinality exactly 1.

An equivalence class defined by E means that, given x, the equivalence class generated by x is the set of all things E-equivalent to x. Everything in one equivalence class is E-equivalent to everything else in that equivalence class. Saying it has cardinality one means that it has one element.

If we did not have criteria #2 in the definition of "equation," then it might be the case that aEb although a and b are different. In that case, the equivalence class generated by a has at least one other element, b; so the cardinality of that equivalence class would not be 1, it would be at least 2.

Looking at the three criteria under #1, it is clear that equality behaves so, and equivalence relations just generalize equality.

In a class where the word equation is defined, soon to follow is the definition of the word solution, as in "a solution to an equation." I haven't thought much about what "solution to an equation" might mean to an ET mathematician.

"it is easy to grow crazy" greeney2
Member
Members
Forum Posts: 10324
Member Since:
April 9, 2009 Offline

On the other hand, they are probably wondering why humans have no idea what equal means, when they can't even balance a check book and stay out of credit card debt.  at1with0
Member
Forum Posts: 9244
Member Since:
April 9, 2009 Offline

cuz it's all about the MONEY

"it is easy to grow crazy" greeney2
Member
Members
Forum Posts: 10324
Member Since:
April 9, 2009 Offline

Check book balance is equal, greater, or less than cost of items to purchase?

Cost of Items to purchase, equal, greater, or less than available credit on card?

I would say simple math, but evidently not when you look at bankruptcy cases. think ET would understand Bankruptcy? at1with0
Member
Forum Posts: 9244
Member Since:
April 9, 2009 Offline

More than simple math goes into bankruptcy, such as human psychology.

I think the ETs already know all the factors that go into it.

"it is easy to grow crazy" khanster
Member
Members
Forum Posts: 713
Member Since:
September 19, 2009 Offline

Equations are definitions. The equals sign can also be seen as the word "is"

For example one added to one is 2 means 1+1 = 2

A FlabberGhost is a FlibberToast is a definition and an equation.

FG = FT  at1with0
Member
Forum Posts: 9244
Member Since:
April 9, 2009 Offline

Well then what does "is" mean (a la Bill Clinton)?

"it is easy to grow crazy"

Forum Timezone: America/Los_Angeles
Most Users Ever Online: 288
Currently Online: angela, Toby
90
Guest(s)
1 Guest(s)
Top Posters:
greeney2: 10324
bionic: 9871
Lashmar: 5290
tigger: 4577
rath: 4298
DIss0n80r: 4162
sandra: 3859
frrostedman: 3816
Wing-Zero: 3279
Tairaa: 2843
Toby
angela
Donald Morgan
Vanessa
ChelseaBrowne
Lincoln
graham day
Angela vara
Will
DLT
Forum Stats:
Groups: 8
Forums: 31
Topics: 9403
Posts: 125016

Member Stats:
Guest Posters: 2
Members: 25164
Moderators: 0