Basic Mathematics - 2020-11-28

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Billy Rubina

05:59

@user21820 I found this question:

A valid argument is only if we have true premises and true conclusion, right?

2 hours later…

General MO7

07:51

HELLO EVERYONE
Would it be possible to analyze exponential graphs using calculus, different series(such as Laplace transform etc) and in case you wanted to know, I am doing newton’s law of cooling.
he idea is that I deriving the equation of newton’s law of cooling but my high school teacher said that it will be a bit easy to derive an equation that could easily be found online so therefore I am thinking of how to make my report a bit more difficult by adding more analysis. Would it be possible? (Any help from you would be very useful

user21820

08:03

@BillyRubina Depends on what is your definition of "valid". In my definition, validity is a purely syntactic matter, so it does not have anything to do with truth in any sense.

A valid proof over ZFC can be meaningless if ZFC proves false statements about ℕ (as interpreted in the real world). Worse still if ZFC proves 0=1.

@GeneralMO7 Trying to obscure things is one form of dishonesty. Instead of trying to make your work seem more difficult, why not ask for more difficult tasks to accomplish?

For example, instead of just dealing with the trivial model that gives you exponential decay, why not make a more accurate model? Even if you assume that a beaker of hot water has uniform temperature, heat is lost not just by conduction but also by evaporation. So you could set up the differential equation to account for that as well.

General MO7

08:29

Well sorry for my dishonesty, can you please give me some inspiration for a harder task involved within newton’s law of cooling

3 hours later…

user21820

11:28

@GeneralMO7 I already gave you a sketch above. If you understand the trivial model that leads to the exponential curve, then you should be able to design a more accurate model that accounts for evaporation in the case of a body of water (such as in a beaker). In particular, what is the rate of heat loss dependent on? It is different for conduction and for evaporation. You can express all that using differential equations.

1 hour later…

Billy Rubina

12:42

@user21820 Yeah, it seems in the book, they use the same definition. They point out that there is a difference between "valid" and "correct". "Valid" depends only on the argument.

user21820

12:58

@BillyRubina Oh okay that's great.

I typically avoid use of that term "valid" because different people use it in different ways. Many times they are not even precise about their meaning.

To be precise and avoid ambiguity we could say "valid/correct proof over S" where S is a formal system.

And for truth we say "true in M" where M is a structure, or "true under I" where I is an interpretation.

Just saying "true" is ambiguous too, and not a good idea.

For statements about the real world, we can say "true in the real world".

Although "the real world" is not a mathematical structure, and hence even that phrase is not precise, it is better than nothing.