# A easy math question.

1. Aug 12, 2010

### zeromodz

If two are equal to a third, do they all equal each other? Can you prove this?

2. Aug 12, 2010

### nicksauce

Depending on what you mean by "two" and "a third", this fact follows from the transitive property.

3. Aug 12, 2010

### Mentallic

I'm going to assume it means if two numbers are equal to 1/3, are the numbers equal?

Well, not necessarily. For them to be equal that means each number has to be 1/6, but of course you can give each number any other value which still satisfies that they add to 1/3.

4. Aug 12, 2010

### Staff: Mentor

The question seems to be ambiguous. I interpret it as nicksauce does, to mean "if two numbers are equal to a third number, then all three are equal."

5. Aug 12, 2010

### Redbelly98

Staff Emeritus
You're interpreting this to mean the sum of two numbers has a value equal to 1/3. Mark44 and nicksauce interpret it to mean that two numbers are each, themself, equal to a third number.

6. Aug 13, 2010

### Mentallic

Oh yeah that seems like a much more reasonable interpretation

7. Aug 13, 2010

### Redbelly98

Staff Emeritus
It's better than my initial thought of "2 = 1/3"

8. Aug 13, 2010

### disregardthat

It's called the principle of explosion. If you grant a false statement, then you can logically prove that any statement is true. Hence your system "explodes" so that the truth values of all statements are 1 (and 0). So if 2 = 1/3, then a = b for any numbers a and b. This can however be proved by mere algebraic manipulation. From 2 = 1/3 you will get 6 = 1, so 5 = 0, or 1 = 0, and from there a - b = 0, so a = b.

EDIT: Oh, after reading the other comments, I realize that the question really was whether a = c, b = c implies a = b. That has been explained.

Last edited: Aug 13, 2010
9. Aug 13, 2010

### slider142

Your original sentence fragment is missing its subject. I assume you mean "If two [objects] are equal to a third [object], ..."
This is true as long as your definition of "equal" shares the transitive property, which is included in the usual mathematical definition of an equivalence between objects.
Specifically, the transitive porperty states that if the relationship between three objects, {a, b, c}, is denoted with the sign "=" such that a = c and b = c, then it follows that a = b.
However, I do not know what your definition of equality is, or what 3 objects you are referring to.
It is quite possible that you are talking about a different kind of equality, which is mathematically more like placing objects into sets.
That is, "A chicken is an animal.", and "A dog is an animal." do not enjoy the transitive property that "A chicken is a dog."