A question about the example used on the Higher-Dimensional Manipulation page

[Verivici]

Isn't 0*infinity an indeterminate value?

 

[Antvasima]

According to the discussions that I have had in private with DontTalk and Alakabamm, as far as I understand, it is still 0.

 

[Antvasima]

According to how DarkLK originally explained it to me as well.

 

[Verivici]

http://mathworld.wolfram.com/Indeterminate.html according to this it is indeed an indeterminate form, wikipedia also refers to it as an indeterminate form

 

[Antvasima]

Okay. I will ask DontTalk, Alakabamm, and DarkLK to take a look at this. If necessary, we will have to rewrite it.

 

[Antvasima]

We are working on solving the problem: https://vsbattles.com/vsbattles/425763

 

[DontTalk]

yes $ 0 \cdot \infty $ is an indeterminate value for the real numbers, since since infinity isn't a real number.

what I mean by times in this context isn't the operation as defined on the real numbers, though. What that the meaning of X*Y in this context is would be more in the direction of "the size of the unification of X sets with size Y".

Technically a more difficult and mathematical explanation would be necessary for complete correctness, but for the casual reader saying it like this is easier to understand than a series of mathematical definitions and proofs, from which most readers wouldn't even understand the symbols.

 

[Verivici]

The cardinality of the sets, you mean? And I think we should at least mention the more complex explanation, maybe put it beneath the simpler one

 

[DontTalk]

Read the pdf about hausdorff dimensions linked for more detailed explanations. (together with a more general script about measurement theory maybe)

 

[DontTalk]

And I don't mean the cardinality of the sets containing the points. When I say "the size of the unification of X sets with size Y" I mean the size as given by a Measure and X as in the amounts of sets with that size that are unified, or in other words as the cardinality of the set that contains the sets that are unified.

(Note: still simplified explanation)

 

[Verivici]

kk

So, have you linked that PDF on the HDM page?

 

[DontTalk]

Yep, it is already linked at the "the concept of a" part.

 

[Verivici]

i see

BTW, do you have a degree in any scientific fields? You seem to be highly knowledgeable.

 

[DontTalk]

No, I don't have a degree in anything. I am studying mathematics since a year now, though.

 

[Antvasima]

Thank you to DontTalk for the help. So, should I close this thread?