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If I have a simple equation such as this:

$$x+5-1=x+4$$

how can I denote that this equation is true? More specifically, if I refer to that equation as P(x), then is there a mathematical notation for saying "P(2) is true"?

Shabbeh
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jeanluc
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  • The equation is true, if on both sides are the same values. Just insert for x the number 2. It becomes 6=6. This equation is true. ${ 2 } \subseteq S$. 2 is subset of the solution set. The equation can be further transformed. – callculus42 Aug 21 '14 at 03:53
  • The notation that you've used seems legit. – Tunococ Aug 21 '14 at 04:09
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    I don't think you need any special exotic notation. English is fine: you just say that "the equation holds when $x=2$, or "$x=2$ is a solution of the equation", or something like that. – bubba Aug 21 '14 at 12:48
  • is there any specific reason why you need one instead of using ordinary language? – Ooker Jun 17 '18 at 16:09

2 Answers2

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One name for an equation that always holds, no matter what values the variables involved take, is an "identity": "$x+5-1=x+4$ is an identity". Really important ones get names: $\sin^2\theta+\cos^2\theta=1$ is the Pythagorean Identity.

If the equation holds only for certain values of the variables -- say $3x + 6 = 0$ -- then you instead say the equation has a solution at $x=2$ (or whatever).

Dan Uznanski
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Beyond calculus's answer, there is not a super short way to write it. If the problem gave you a domain, you can write that the input is a member of the domain. Or, if it is not a too rigorous mathematics course, you can show that 1=1 when you have a particular x value.

user170141
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