- #1
zeromodz
- 246
- 0
If two are equal to a third, do they all equal each other? Can you prove this?
Proving Equality in Math: Solving the Question of Two Equaling a Third
- Thread starter zeromodz
- Start date
In summary, depending on the definition of "two" and "a third", the fact that if two numbers are equal to a third, then they are all equal to each other follows from the transitive property. However, this may not be the case if a different type of equality is being used, such as placing objects into sets.
- #2
nicksauce
Science Advisor
Homework Helper
- 1,271
- 7
Depending on what you mean by "two" and "a third", this fact follows from the transitive property.
- #3
Mentallic
Homework Helper
- 3,802
- 95
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.
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
Mark44
Mentor
- 37,806
- 10,208
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
- 12,180
- 186
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.Mentallic said:
- #6
Mentallic
Homework Helper
- 3,802
- 95
Oh yeah that seems like a much more reasonable interpretation 
- #7
- 12,180
- 186
It's better than my initial thought of "2 = 1/3"
- #8
disregardthat
Science Advisor
- 1,866
- 34
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.
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:
- #9
slider142
- 1,017
- 72
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."
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."
FAQ: Proving Equality in Math: Solving the Question of Two Equaling a Third
What is the answer to the easy math question?
The answer to the easy math question depends on what the question is. Without knowing the specific question, I cannot provide an answer.
Is the easy math question suitable for all ages?
This would depend on the complexity of the question. Some easy math questions may be suitable for all ages, while others may require prior knowledge or development of certain math skills.
Can you give an example of an easy math question?
An example of an easy math question could be: What is the sum of 2 + 2?
Do I need any special tools or equipment to answer the easy math question?
No, typically easy math questions can be solved using basic mental math or with a pencil and paper.
Why is it important to answer easy math questions?
Answering easy math questions helps to develop and maintain basic math skills, which can be beneficial in everyday life and in more complex math problems.