A=B=C
is one equation.

A=B
B=C
are two equations.

A=B
B=C
A=C
are three equations.

 

A=B=C
is one equation.

A=B
B=C
are two equations.

A=B
B=C
A=C
are three equations.

So what is the definition of "equation" that you are using. In particular, what definition supports the claim that A=B=C is but one equation?

 

The difference is the number of equalities.
The first can convey 1 bit, the second 2.

 

It's been a real long time....I was taught that an equation was a statement of equality.

The statement may be true or false.

 

The difference is the number of equalities.
The first can convey 1 bit, the second 2.

That makes no sense.

 

It's a no brainer and simply a statement of "Transitivity".

 

It's a no brainer and simply a statement of "Transitivity".

Is it a no brainer?

So what's your opinion. How many equations are represented by A=B=C (and, again, A,B, and C are placeholders for expressions) and what is the basis for that answer and why aren't the other answers that have been offered correct? The general options are 1, 2, or 3 (with more than three being an option to discuss if you want to).

 

WBhan, I am by no means an expert of math or anything close.

I never did find out what the new math was, and that was along time ago.

Plugging in all the numbers and manipulation is fun for some, but the whole idea is to see if equality is true or false.

The equality/equation A=B=C has only two states. One bit.

Two equations have four states. Need 2 bits.

Consider this. The first equation is one state, the second equations require two states. Even when the two are equal, that does not prove that A=B=C.

Also beware that the extra events and states can be carried further onto/into averages, and statistical and probability data. All this while giving a false positive.

I was not aware that an equality came in pairs only.

I am really behind, pardon me.

 

A=B=C
is one equation.

In my world, it's a shorthand representation for two equations.

A=B
B=C
are two equations.

Agreed.

A=B
B=C
A=C
are three equations.

Again in my world, that's two equations rearranged to produce a third. So yes, 3 equations, but with an asterisk since only 2 are independent.

 

But I have to admit that

x ≤ y ≤ z
​

is a single equation. Hmmm...

 

Still, it depends... No one has included in their responses, what definition of equation they are using. I present this one definition fron Dr. Math.

"An equation is a mathematical "sentence" that says that two things are equal. <omitted simple linear equation example>

An equation consists of two expressions connected by an equals sign. It can only be true or false" [Note: the equation as a whole is true or false; not it's solution]

The statement x ≤ y ≤ z is an inequality, defining the relation between the variables or expressions x, y, and z. Hence, it is not an equation. Equations deal with equalities.

 

But I have to admit that

x ≤ y ≤ z
​

is a single equation. Hmmm...

Why? How is it any different from

x ≤ y
y ≤ z

 

It's not! Somehow, to my eyes, the inequalities and the expression that y is between x and z is a single equation whereas the equalities make x=y=z into two. I can't really defend it or say just why.

 

I see three, but being a math brick I can't argue it either way. Don't forget x=z.