Definitions are not Free!

[dimreepr]

1 hour ago, Willem F Esterhuyse said:

I actually saw the symbols the second time I verified it. The first time I went on feeling.

Then they're only hidden from the rest of us; and, it seems, your not capable of explaining it to anyone, so what's the point of this thread?

You may as well be describing fairies, to a trampoline...

Edited January 2, 2023 by dimreepr

[Willem F Esterhuyse]

4 minutes ago, dimreepr said:

Then they're only hidden from the rest of us; and, it seems, your not capable of explaining it to anyone, so what's the point of this thread?

I can try to start to externalize it (by suspending disbelief), if you need such a point. There is another point to the thread.

[dimreepr]

8 minutes ago, Willem F Esterhuyse said:

I can try to start to externalize it (by suspending disbelief)

You can suspend your disbelief, but I'm gonna need to see the fairy.

10 minutes ago, Willem F Esterhuyse said:

There is another point to the thread.

Which is?

All I can see is a troll...

[Willem F Esterhuyse]

13 minutes ago, dimreepr said:

Which is?

That definitions are not free!

[dimreepr]

4 minutes ago, Willem F Esterhuyse said:

That definitions are not free!

Define free.

[studiot]

On 12/31/2022 at 12:16 PM, Willem F Esterhuyse said:

It does not contribute to the question of right and wrong definitions.

You just gave two examples in Logic, didn't answer the question.

Your opening post contained an assertion that I challenged since it is not completely true.

I gave you a counterexample.

 

I did not only answer your question but posted in such a way as could not be (I thought) mistaken for anything other than an answer to the question you asked, which I identified by the question mark you provided in your opening post.

 

On 12/14/2022 at 1:00 PM, studiot said:

On 12/14/2022 at 12:31 PM, Willem F Esterhuyse said:

Now I wonder if the same applies to Mathematics?

 

Apart from the mathematical versions of the above examples, what about statistics and probability ?

 

This time I provided two further counter examples to the false statement you started with as pertinent to explaining why I made the answer I did.

Edited January 2, 2023 by studiot

[Willem F Esterhuyse]

38 minutes ago, studiot said:

Your opening post contained an assertion that I challenged since it is not completely true.

So please specify, for example, definitions in statistics and probability that are free. I can see that there is a free definition in the Liar Paradox.

49 minutes ago, dimreepr said:

Define free.

Not following any proven law.

[dimreepr]

12 minutes ago, Willem F Esterhuyse said:

Not following any proven law.

Imagine that.

[Genady]

Is a definition of Dirac delta function free?

Which proven law does it follow?

[studiot]

7 hours ago, Willem F Esterhuyse said:

So please specify, for example, definitions in statistics and probability that are free. I can see that there is a free definition in the Liar Paradox.

'Free'  is your word not mine.

And since I don't fully understand what you mean I can't offer definitions in statistics or probability that are 'free'

The liar paradox example offers you a statement whose truth value is undecidable. That is why it is a counterexample to your assertion.

Note the terms 'wrong' and 'right' are not really technical ones.  False and True are preferable in both formal logic and formal mathematics.

 

As regards why statistics and probability offer counterexampls; it is because they necessitate multiple outputs or values for a given input.
In other words they represent a range of values rather than the plain binary 'true or false' with nothing in between.

You are still ignoring both tristate and fuzzy logic which have yet further ways of denoting multiple or ranges of values and also independence or what engineers call the 'don't care values' in the truth table.

Edited January 2, 2023 by studiot

[Willem F Esterhuyse]

19 hours ago, Genady said:

Which proven law does it follow?

I think it follows the law that: 0*infinity = 1. 0*infinity could = 1 since 0*infinity = finite number.

 

12 hours ago, studiot said:

Note the terms 'wrong' and 'right' are not really technical ones.

A definition is wrong if it leads to an unsound system.

Edited January 3, 2023 by Willem F Esterhuyse

[Genady]

4 minutes ago, Willem F Esterhuyse said:

I think it follows the law that: 0*infinity = 1

Is it a proven law? I think, this equation is incorrect.

For example, x*log(x)→0 when x→0 and log(x)→-∞.

[Willem F Esterhuyse]

Dirac Delta function requires integral(-inf->inf) delta(x) dx = 1 and this requires 0*inf = 1. The question is how fast it tends to inf and zero. log x tends faster to -inf than x tends to zero so x*log x must-> -inf. 0*anything = 0 does not hold for "anything" being inf.

inf = infinity.

[studiot]

49 minutes ago, Willem F Esterhuyse said:

A definition is wrong if it leads to an unsound system.

 

This is most definitely a flawed definition of 'wrong'

There are cases you should have considered before you made it.

 

50 minutes ago, Willem F Esterhuyse said:

I think it follows the law that: 0*infinity = 1. 0*infinity could = 1 since 0*infinity = finite number.

I agree with Genady.

All these statements are only true in a few specialised number systems.

They are certainly not true in any system up to and including the Real number system.

[Genady]

Which proven law does definition of imaginary number "i" follow?

[Willem F Esterhuyse]

1 hour ago, Genady said:

Which proven law does definition of imaginary number "i" follow?

That a number can be given a letter name.

[studiot]

3 minutes ago, Willem F Esterhuyse said:

That a number can be given a letter name.

A name is not the number itself, anymore than 

are the number we call four.

 

They are all representations.

 

[Genady]

1 hour ago, Willem F Esterhuyse said:

That a number can be given a letter name.

Like @studiot said, the letter does not matter. In this case, scientists and mathematicians call it "i" while engineers call the same number, "j".