can I use them together

[Cjoseph]

In what context can I use this 2 symbols together ∴ ∃ ?

 

[topsquark]

In what context can I use this 2 symbols together ∴ ∃ ?

The symbols are read as "therefore" and "there exists." So as an example you could say that [math]x^2 + 2x - 3 = 0[/math] can be solved by the quadratic equation, [math]\therefore \exists[/math] a solution.

(This example reads a bit funny but it works.)

-Dan

 

[Steven G]

I 2nd what Dan said.

... therefore there exists...

Do you know what \(\displaystyle \exists!\) means?

 

[Cjoseph]

I 2nd what Dan said.

... therefore there exists...

Do you know what \(\displaystyle \exists!\) means?

No I don't, do you mind explaining that symbol as well.

 

[Cjoseph]

The symbols are read as "therefore" and "there exists." So as an example you could say that [math]x^2 + 2x - 3 = 0[/math] can be solved by the quadratic equation, [math]\therefore \exists[/math] a solution.

(This example reads a bit funny but it works.)

-Dan

Thank you for your explanation. Also, is it frequently to see those symbols together? Can I use those 2 symbols together to prove a theorem?

 

[Steven G]

No I don't, do you mind explaining that symbol as well.

There exists a unique

 

[pka]

There exists a unique

Here is a true story. I took a first course in symbolic logic from a Copi trained (PhD from Yale) professor.
On a test I used the \(\displaystyle \exists !(x)\) for "there exists an unique x". He marked it wrong.
He told me that uniqueness is coded as \(\displaystyle (\exists x)(\forall y)[ P(x)\wedge(P(y)\to(x=y))]\)