# This symbol ⇔

## Main Question or Discussion Point

i don't undestand this ⇔ on physics and math x + 5 = y + 2 ⇔ x + 3 = y i don't rember the physical equation that uses it.

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davenn
Gold Member
2019 Award
i don't undestand this ⇔ on physics and math x + 5 = y + 2 ⇔ x + 3 = y i don't rember the physical equation that uses it.
from my understanding.....
it is saying what is on the left is the same as ( equivalent to) what is on the right of the sign

Dale
Mentor
i don't undestand this ⇔ on physics and math x + 5 = y + 2 ⇔ x + 3 = y i don't rember the physical equation that uses it.
It means "if and only if". I.E. logical equivalence. The expression on the left is true if the expression on the right is true, and the expression on the left is true only if the expression on the right is true.

HallsofIvy
Homework Helper
i don't undestand this ⇔ on physics and math x + 5 = y + 2 ⇔ x + 3 = y i don't rember the physical equation that uses it.
In this particular example, if x+ 5= y+ 2 then subtracting 2 from both sides, x+ 3= y. Conversely, if x+ 3= y then adding 2 to both sides gives x+ 5= y+ 2. That is, if x+ 5= y+ 2 is true, then so is x+ 3= y and, conversely, if x+ 3= y is true then so is x+ 5= y+ 2. Each side implies the other.

davenn
Gold Member
2019 Award
thanks guys :)

Well, I've learned something today. I shall most certainly be using this in maths, it will cut down on the amount of bull I write!

HallsofIvy
Homework Helper
Just a slight addition: "y= 3=> y^2= 9" but it is NOT true that "y= 3 <=> y^2= 9" because it is not true that "y^2= 9=> y= 3". If y^2= 9 y itself may be 3 or -3.

sophiecentaur
Gold Member
It means "if and only if". I.E. logical equivalence.
That was IFF on my analysis course. Is that not used any more?

Just a slight addition: "y= 3=> y^2= 9" but it is NOT true that "y= 3 <=> y^2= 9" because it is not true that "y^2= 9=> y= 3". If y^2= 9 y itself may be 3 or -3.
So am I right in thinking that A<=>B means that if A is true, B is true and vice versa whereas A=>B means if A is true, B is true but B does not make A true?

You could think left hand expression => right hand expression as left hand expression implies right hand expression
left hand expression <= right hand expression as left hand expression is implied by right hand expression
So left hand expression <=> right hand expression is LHE implies and is implied by RHE.

Dale
Mentor
That was IFF on my analysis course. Is that not used any more?
I think both are used. It just depends on a particular authors preferences.

sophiecentaur