Equals Sign with a Dot or a ~ Over It

Date: 01/25/2001 at 16:45:26
From: J. Leon Shohet
Subject: Meaning of a special equal sign

What does an equals sign with a dot (.) over it mean?

Date: 01/26/2001 at 16:39:35
From: Doctor Ian
Subject: Re: Meaning of a special equal sign

Hi,

That symbol means 'is nearly equal to'.  

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/   

Date: 12/04/2001 at 10:26:47
From: Kyle Lawrence
Subject: A symbol I don't know

What does an equals sign with a ~ over it mean?

Date: 12/04/2001 at 12:39:19
From: Doctor Ian
Subject: Re: A symbol I don't know

Hi Kyle,

It means 'approximately equals'.  For example, the value of pi is 
approximately 3.14, so we might write

     ~
  pi = 3.14

It's a subtle distinction, but an important one. Ignoring it can lead 
you to results like this:

    x^2 = 2
 
      x = sqrt(2)

      x = 1.41

  x * x = 1.41 * 1.41

    x^2 = 1.98

      2 = 1.98

Note the difference:

    x^2 = 2
 

      x = sqrt(2)

        ~
      x = 1.41

        ~
  x * x = 1.41 * 1.41

        ~
    x^2 = 1.98

        ~
      2 = 1.98

Does this help?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/