Trouble Remembering Physics Equation with x + 5 = y + 2 and x + 3 = y

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Discussion Overview

The discussion revolves around the interpretation of the equations x + 5 = y + 2 and x + 3 = y, particularly in the context of logical equivalence and implications in mathematics and physics. Participants explore the meaning of these equations and their relationships, as well as the broader implications of logical statements.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants express confusion about the physical equation related to x + 5 = y + 2 and x + 3 = y.
  • One participant suggests that the equations indicate logical equivalence, meaning each expression is true if and only if the other is true.
  • Another participant elaborates that if x + 5 = y + 2, then x + 3 = y follows, and vice versa, emphasizing the bidirectional implication.
  • There are mentions of the notation "iff" (if and only if) and its usage in analysis courses, with some questioning its current relevance.
  • A participant introduces a related example involving y = 3 and y^2 = 9 to illustrate the nuances of logical implications and equivalences.
  • Discussions arise about the differences between "A <=> B" and "A => B," with participants attempting to clarify these logical relationships.

Areas of Agreement / Disagreement

Participants generally agree on the concept of logical equivalence and implications, but there is some uncertainty regarding the terminology and its usage in different contexts. The discussion remains somewhat unresolved regarding the clarity of these concepts and their application.

Contextual Notes

Some participants express uncertainty about the physical equation's relevance and the implications of logical statements, indicating a need for clearer definitions and examples.

Who May Find This Useful

This discussion may be useful for students or individuals interested in understanding logical equivalence and implications in mathematics and physics, particularly those studying related concepts in academic settings.

Davi da Silva
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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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Davi da Silva said:
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
 
Davi da Silva said:
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.
 
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Davi da Silva said:
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.
 
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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!
 
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.
 
DaleSpam said:
It means "if and only if". I.E. logical equivalence.
That was IFF on my analysis course. Is that not used any more?
 
HallsofIvy said:
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?
 
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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.
 
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sophiecentaur said:
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.
 
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DaleSpam said:
I think both are used. It just depends on a particular authors preferences.
IFF you say so! :wink:
 
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