Symmetric Property

mathdad

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If 2 = x, why does x = 2?

The reason is the symmetric property.
Can this property be applied as shown below?

Is 1-5 symmetric?

1. If a = b, then b = a.

2. If f(x) = y, then y = f(x).

3. If A = LW, then LW = A.

4. If F = ma, then ma = F.

5. If sqrt{x^2} = x, then x = sqrt{x^2}.

Correct?
 
If 2 = x, why does x = 2?
The reason is the symmetric property.
Can this property be applied as shown below?
The common way of reading \(\displaystyle x=2\), "x is 2."
Do you know what the definition of "is" is?
 
If 2 = x, why does x = 2?

The reason is the symmetric property.
Can this property be applied as shown below?

Is 1-5 symmetric?

1. If a = b, then b = a.

2. If f(x) = y, then y = f(x).

3. If A = LW, then LW = A.

4. If F = ma, then ma = F.

5. If sqrt{x^2} = x, then x = sqrt{x^2}.

Correct?
Yes, all those conditional statements are true, and are examples of the symmetric property of equality. (I wouldn't say literally that they "are symmetric", however.)

Many students misunderstand "=" and think of it in an asymmetric way, as if 2 + 3 = 5 meant "the result of adding 2 and 3 is 5"; this thinking results in "run-on equations" like "2 + 3 = 5 + 2 = 7" to represent a sequence of operations. That is wrong.

In formulas, like F = ma or f(x) = x+1, it often carries the implication that either F is found by doing ..., or "f is defined as ...". But in all of these cases, all it really means is "____ has the same value as ___". And that is necessarily symmetric: if this and that have the same value, then that and this have the same value.
 
The common way of reading \(\displaystyle x=2\), "x is 2."
Do you know what the definition of "is" is?

Come on, pka. Of course, I know what the word "is" stands for in math.
 
Yes, all those conditional statements are true, and are examples of the symmetric property of equality. (I wouldn't say literally that they "are symmetric", however.)

Many students misunderstand "=" and think of it in an asymmetric way, as if 2 + 3 = 5 meant "the result of adding 2 and 3 is 5"; this thinking results in "run-on equations" like "2 + 3 = 5 + 2 = 7" to represent a sequence of operations. That is wrong.

In formulas, like F = ma or f(x) = x+1, it often carries the implication that either F is found by doing ..., or "f is defined as ...". But in all of these cases, all it really means is "____ has the same value as ___". And that is necessarily symmetric: if this and that have the same value, then that and this have the same value.

Interesting notes for my files. Thanks. I will post more properties with examples in the coming days.
 
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