limit proving

[Johnny5]

Dave, what is the definition of continuity please.

 

 

Thank you.

[Dave]

[math]\forall \epsilon > 0 \exists \delta > 0 \text{ such that } |x-c| < \delta \Rightarrow |f(x) - f©| < \epsilon[/math].

[Johnny5]

Dave,

 

What is the symbol in latex for 'if then'?

 

Also, what is mathbb? I saw it give the symbol for the natural numbers.

[Dave]

What, [math]A \Rightarrow B[/math]? This means "A implies B".

[Johnny5]

What, [math]A \Rightarrow B[/math']? This means "A implies B".

 

Yes well sometimes there is a single line arrow used for ifthen

 

When an ifthen is known to be true, then the double arrow is used.

 

Perhaps I didn't say that right...

 

 

Here is a truth functional definition of -->

 

XY X-->Y

00 1

01 1

10 0

11 1

 

Here is a truth functional definition of <-->

 

XY X<-->Y

00 1

01 0

10 0

11 1

 

Now, in the case where A <--> B is a tautology, the thicker arrow is used

 

In the case where A-->B is a tautology, the thicker arrow is used.

 

Do you have any idea what I'm talking about?

 

 

It's just a notation-type question thats all I'm asking.

[Dave]

You might want to take a look here: http://omega.albany.edu:8008/Symbols.html

 

There's a load of symbols there. If you can't find it, google for "latex symbols", and a load of sites should pop up.

[Johnny5]

You might want to take a look here: http://omega.albany.edu:8008/Symbols.html

 

There's a load of symbols there. If you can't find it' date=' google for "latex symbols", and a load of sites should pop up.[/quote']

 

Unfortunately, for some reason the site didn't load, so I couldn't see the list of symbols there.

 

[math]A \Rightarrow B[/math]

 

See how there are two lines running right/left, is there a Latex symbol for an arrow with just one line?

[Dave]

Sure, you can use [math]\rightarrow[/math].

[Johnny5]

Ok Dave, do you differentiate between the meaning of

 

[math]\rightarrow[/math]

 

and the meaning of

 

[math] \Rightarrow [/math]

 

Just a simple yes or no will do. You can add an explanation if you feel it is warranted.

 

 

Thank you.

[Dave]

Well, yes; in general I think of the top one being "towards" as in "x tends towards 0", and the lower being implies.

[Johnny5]

I meant when using them as logical operators.

[Dave]

I can't say I've ever used the top one as logical operator.

[Johnny5]

I know how to answer my own question then...

 

Dave, what is the definition of

 

[math] \Rightarrow [/math]

 

Now I will find out what I want to know.

 

Thank you

[Dave]

[math]A \Rightarrow B[/math] "means" [math](\neg A) \vee B[/math].

[Johnny5]

Ok, i have my answer.

 

Would you mind listing the symbols which you use to denote the logical operators, or perhaps you know them as logical connectives?

 

Thank you

[Dave]

I've not done a lot in the area of boolean algebra/logic to be perfectly honest. The only ones I really know are:

 

[math]\neg[/math] - not

[math]\wedge[/math] - and

[math]\vee[/math] - or

[math]\Rightarrow[/math] - implies

 

But that's about it. I'm aware of other ones (like xor, etc) but I don't know symbols for them I'm afraid

[Johnny5]

I know all of the ones you listed. Let me ask you something, how many different ones are possible? Do you know, is it 5,6,7,8,9 how many?

 

Oh and by the way the symbol for XOR is...

 

[math] \underline \vee [/math]

 

Also do you use any other symbol besides [math] \neg [/math] to denote the logical connective... NOT

 

?

 

Also I use the sheffer stroke / for NAND

 

And umm...

 

 

oh yes this symbol for NOR |

 

A nor B = A|B

 

NAND does not appear in my written work for some reason though.

 

But I do use XOR on occasion, it seems to alleviate some difficulties every now and then.

 

Oh, and how good are you in first order logic?

[Dave]

Not particularly brilliant We've only had one lecture course that even covered it, and when we did cover it, it was only for a week.

[Johnny5]

Not particularly brilliant We've only had one lecture course that even covered it, and when we did cover it, it was only for a week.

 

Well figure out how many different logical connectives there are for me if you can. I think the answer is nine.

 

Regards

 

1. nor

2. nand

3. not

4. and

5. or

6. xor

7. if-then

8. if and only if

9. nif (not if-then)

 

I think this is all of them