Mathematics is entirely (almost) based on Logic and cosequentially on Set Theory. What Gödel showed was that our system of arithmetic and algebra is not always consistent and must occasionally appeal to outside of the system to produce results that are true in the real world.

For instance 0! must be valued at 1 in order for the math to come out correct. You can see this from the Binomial Theorem for example.

Any course in Logic will include Gödel's work along with the set theoretic Zermelo-Fraenkel axiomatic system (with choice).

My logic masters, Ludovico Geymonat, Corrado Mangione, Pier Giorgio Odifreddi insist that logic is not a subset of mathematics but a discipline of its own. I agree with them.
Tullio

---

For instance 0! must be valued at 1 in order for the math to come out correct.

You are confusing ordinals with cardinals.
Zero is the first integer and called first in cardinals.
Then comes second, third...
https://en.wikipedia.org/wiki/Cardinal_number
Actually this is a hint to my quiz:)

@ Tullio.
I Think mathematics is a subset of logic.

Yes it can be the chicken instead of the egg. Logic is a discipline and when applied can produce most of Mathematics.

When computing probabilities you can construct the Venn Diagram which embodies Set Theory which follows directly from Logic. These can all be considered to be Disciplines in their own right. This does not mean that they are not related nor that one can represent and explain another of these.

Boolean Logic which is the foundation for base 2 arithmetic (Mathematics), logic and how our computers work is represented well by this example in two variables:



I suppose that pure mathematicians get all huffy and bent out of shape when someone dares to apply their beautiful, abstract creations to useful purposes.

"Here's to pure mathematics ; may it never be of use to anybody." Anonymous

I suppose that pure mathematicians get all huffy and bent out of shape when someone dares to apply their beautiful, abstract creations to useful purposes.

"Here's to pure mathematics ; may it never be of use to anybody." Anonymous

I know this toast of Cambridge Cavendish Laboratory (1897):
To the electron; may it never be useful to anybody!
Tullio

---

When at school we had applied maths and pure maths lessons. We could see the point of applied maths, but pure maths was just maths for the sake of it.

Unless that math leads you to split the atom or better yet fuse two of them together. Applied math would never get you there.

---

Bob DeWoody

My motto: Never do today what you can put off until tomorrow as it may not be required. This no longer applies in light of current events.

Applied math would never get you there.

What?
Applied math is the basic tool in physics.
http://space.mit.edu/home/tegmark/mathematical.html

Unless that math leads you to split the atom or better yet fuse two of them together.

It was Lise Meintner that found out how to split the atom.
She was not a mathematician.
Her colleague Otto Hahn got the Nobel Prize for that finding.
She moved to Kungälv Sweden from Germany because she was a jew in the 30's.
https://en.wikipedia.org/wiki/Lise_Meitner

It was Einstein that realized that fusion of atoms can transform mass to energy. E=MC2
Pure math.

https://en.wikipedia.org/wiki/Immanuel_Kant

Do not forget this man either.

It wa Enrico Fermi and his group in Rome to split the uranium nucleus with slow neutrons, but they did not recognize what they had done. God in His wisdom, made us all blind, said Emilio Segre'. It was a woman, Ida Noddack, a Czek chemist, to understand what Fermi had done but she was not believed. Then Lise Meitner and Otto Hahn gave the correct interpretation of Fermi's result and they were believed.
Tullio

---

Welcome back to the project, Chris.

---

rOZZ
Music
Pictures

I gave up on pure maths when I struggled with integration and differentiation at school! Applying formulas to practical physics problems like speed, motion, acceleration, & coefficient of friction was fine, but what was the point of solving quadratic equations like ax^2 + bx + c = 0? Ok they make pretty graphs but .....

ax^2 + bx + c = 0 is a simple example how to solve a polynom. Nothing else.

The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus states that antidifferentiation is the same as integration. Differentiation and integration constitute the two fundamental operations in single-variable calculus.

If you do an integration of Newton's F=m*a you get the momentum P=m*v.
One more integration and you get the kinetic energy E=m*v*v/2.
Is that philosophy or a mind game Chris?

What I want is someone to tell me how philosophy with mind games has benefited the world.

I Think you know the answer by asking the very philosophic question:
Are we alone in the universe?

It is good to see a thread on Philosophy in the Science corner. In my opinion Philosophy cannot be seen as a pseudo-science. It complements the actual sciences such as Maths, Fyzix, etc. The problem with Philosophy, in my opinion, is the different opinions of different individuals with no basic truth they can rely on except for the ancient philosophers, but who says that they were right?

---

rOZZ
Music
Pictures

F=dp/dt.p(momentum)=mv. So F = mdv/dt + vdm/dt. This is the case of a rocket whose mass changes because the fuel is being burned. So F is not simply ma (a acceleration). This in Newton dynamixcs.
Tullio

---

It is good to see a thread on Philosophy in the Science corner. In my opinion Philosophy cannot be seen as a pseudo-science. It complements the actual sciences such as Maths, Fyzix, etc. The problem with Philosophy, in my opinion, is the different opinions of different individuals with no basic truth they can rely on except for the ancient philosophers, but who says that they were right?

Basic truth?
We don't even no what reality is.
Do we know what nothing is? That has been discussed for over 2500 years.
And what is infinity and a singularity?
Do they exist?
I don't Think anybody has been there:)

Read Bernard d'Espagnat "A la recherche du reel, Le regard d'un physicien", 1981, Bordas, Paris.
Tullio

---

F=dp/dt.p(momentum)=mv. So F = mdv/dt + vdm/dt. This is the case of a rocket whose mass changes because the fuel is being burned. So F is not simply ma (a acceleration). This in Newton dynamixcs.
Tullio

True. But your example is a special case.
Now if you increase the speed to near the speed of light the mass increases:)

Correction of your equation:
F = (dm/dt)*(dv/dt )

Read Bernard d'Espagnat "A la recherche du reel, Le regard d'un physicien", 1981, Bordas, Paris.
Tullio

I have seen TV shows from BBC Horizon and Morgan Freeman's Through a Wormhole where scientists are trying to explain these matters:)

I said I used Newton dynamics, leaving Einstein aside.
Tullio

---

I said I used Newton dynamics, leaving Einstein aside.
Tullio

Hehehe.
Anyway. I Think your rocket example should be like this F = (dm/dt)*(dv/dt )