Do Earth and Martian Mathematicians Understand Limits Differently?

[Organic]

A Marsian mathematician visiting Earth and wishes to understand how Earthman mathematician understand the limit concept.

After couple of hours of communication we have this situation:

1) a not= b

Earthman: By my way (1) is an hypothesis.

Marsian: By my way (1) is an invariant state.

2) abs(a-b)=d < e > 0

Earthman: a) By my way you compare d to set S that includes in it all R members > 0. in this case d<d is impossible; therefore d must be = 0 --> a=b

Earthman: b) Another version of my way is to say that e=d/2 but then |a-b|=d AND |a-b|<d/2 which is impossible; therefore a=b.

Marsian: e and d relation remaining unchanged in any arbitrary scale that you choose, which means: d is always smaller then e but greater than 0. It means that e=d/2 is impossible because e > d/n > 0.

Marsian: S is an open collection (has infinitely many elements) therefore cannot be completed by definition. Only finite collection can be a complete collection. Therefore there is no such thing like S which includes all r > 0.

Earthman: How a set cannot be completed? for example: please explain how N is not a complete collection of all n's by showing me n which is not in N.

Marsian: Natural numbers do not exist because of the existence of N, but because of the axioms that define them, N is only the name of the container that its content is infinitely many elements that can never be completed, and defined by the proper axiomatic system.

Earthman: e and d are fixed values.

Marsian: e and d are variables, and both of them are always greater than 0.

Options:

a) Earthman method is the right method.

b) Marsian method is the right method.

c) There is no one right method; therefore both methods are reasonable methods.

Please choose a, b or c or if you like, please add more options.

When you choosing or adding some option, please explain why do you choosing or adding it?

Thank you,

Organic

 

[Zurtex]

MY Question: What is a Marsian, do you perhaps mean a Martian?

 

[matt grime]

Very little of what you've written is an accurate reflection of the actual question, which is that

if a and b are real numbers and if for every e>0 we know |a-b|<e, then this implies a=b.

I'm sorry you cannot understand how proof by contradiction works. By the way, for those who need to know what invariant state means, as it's one of the new fangled terms just invented by Organic, it apparently means it is unchanged when you zoom in. Quite how one defines zooming in on a proposition is not clear.

I would like it if a logician gave the correct terms for things like e, which ought to be something like a quantified something or other.

And if anyone wants to know where d comes from it all arises from the proof of the proposition that runs:

suppose a is not b (ie take the negation of the conclusion), then as |a-b|=d is a strictly positive number, we see that

|a-b|<d by hypothesis, therefore as d<d is a contradiction, it follows that the supposition that a=\=b is false, hence a=b.

The other way, possibly preferable as it removes the unnecessary contradictory part, is to interpret that as saying that the statement |a-b|<e for all e>0 is false, thus the negation of the conclusion implies the negation of the initial hypothesis, hence, taking the negation of that we see the proposition is true.

Organic's rough argument is that |a-b| =d and letting d=e is "meaningless" as it cannot happen. That is he is presuming the result to prove the result.

Anyone care to explain the concept of proof and such? Cos it won't be me this time.

Forgot to say that d is fixed in the sense it is |a-b| and they are given real numbers and e is a free variable, quantified by "for all", wish I could remember all the predicate, quantified, undefined imprimitive terminology.

Oh, and don't expect this won't move to TD either Organic if you're going to insist on not using terms correctly, such as "all" and "complete" and so on.

 

[Organic]

MY Question: What is a Marsian, do you perhaps mean a Martian?

A Matrian calls himself a Marsian.

 

[Zurtex]

So what does Earthman and Marsian each think the basic upshot is of what they have supposedly proved?

 

[Organic]

Please write what do you think.

 

[Zurtex]

Please write what do you think.

This is your maths to justify not mine.

 

[Organic]

Zurtex,

I am not justifying anything, please read all what has been written until now and write your opinion and also, if you want, why this is your opinion?

Thank you.

 

[moshek]

Well Organic you present here two different attitude to mathematics
and by a dialog the concept of limit may became more flexible than in know to Earth mathematitian. So there is no right or wrong here, I choose (c)


Moshek

 

[moshek]

Organic:

I see they move you also from mathematics like they did to Lorentz.
I am really sorry for you. please don't give-up to share your discoveries with us One day they will be sorry they did that to you. My sort article is for you now.

Yours
Moshek


Intelligent life

Planet Mar's was connected twice to the search of man for intelligent life. First was the effort to understand the retrograde movement of Mars on the background of the night sky. second was a mistake that identify cannel on is face done by other culture. maybe there is connection between Mars to the search of life in the area of mathematics.
Thousand year's ago people observed that Mars is going sometime in the opposite direction relative to the stars. Mars is moving slowly on the background of the night sky so you can distingue the different every day, suddenly he stand and then start to go in the opposite direction. Then he stop again and continue his regular direction.
For explaining this strange movement the astronomer invented complex system of wheels so that Earth is in the center . the most complicate system was invented by Talmy and it included 12 wheels. But 400 year's ago Copernicus invent a new revolutionary idea so that put the sun in the center of the world and not the planet earth. In this observation the explanation to the movement of mar's became very simple and it base on some interaction of movement between mar's and earth. This is how the science revolution started and it was with many hard struggle. The follower of Copernicus, Galilo and Newoton base the science way of thinking by a development of a new suitable mathematics.
The top of this way of thinking bring in the 20 century to the development of two central theory: Relativity and Quantum theory. These two theory's change the way man understood himself in the world. We are not passive observer in the phenomena , and we have some active part that base on the interaction that between us and the world. Is there a way to establish similar principle in the rational area of mathematics? By first looking it look that there is no way for doing this. The world of mathematics seems to be absolute and exist without man. But from the other side we know that here is today some need to develop a new looking to mathematics that can bring to more understanding of the relation between mathematics and the world of phenomena. This was express in the lecture of Alein Connes who develop 20 year's ago Non commutative Geometry, and consider as one of the leading mathematician in the world today. "… we need today a new understanding in mathematics that it's source is not necessarily come from logic but more on the geometry." This end the last lecture in the conference "100 to Hilbert" . This conference was to point another famous lecture of Hilbert in Paris in 1900. Hilbert end his lecture by drawing a vision to discover an organic unity of mathematics.
A Common looking on those two important conference like two eye's, one took place in Paris and the other in Los-angels, with a different of 100 year's in time arise the question if and how is moving mathematics , like mars, on the background of the culture of mankind. This is how arise the problem that not solved yet , of the inherent hidden connection between mathematics and the real world. But like the observation of Copernicus that aloud us to put the Sun in the center of our world and by this to understand more simply the interaction between the Earth and mar's, we can point to a third eye's that solved the mathematical problem. The new common center of mathematics and physics is the discovery of the organic unity of mathematics , intelligent life.

 

[Organic]

My dear Moshek,

Thank you very much for your support, because as you see the middle ages are still in the minds of current professional mathematicians society.

But as long as I know my name, I'll continue to air my view.

This time they moved my post here, without leaving any tracks that it was originally opened in the Mathematics forum under "geneneral Math".

 

[moshek]

I can't believe they did that to you Organic !
When your threads are the most readable
and also respond here!

When the picture of Albert Eintein is use here.

I am really sad now .

Moshek

 

[moshek]

Einstein , sorry