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Organic
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Martian mathematician visiting Earth, and he wishes to know how an Earthman mathematician understanding the limit concept.
After couple of hours of communication we get this situation:
1) a not= b
Earthman: By my way (1) is a hypothesis.
Martian: 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.
Martian: 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.
Martian: 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 can a set be not completed? For example: please show us n which is not in N.
Martian: 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.
Martian: e and d are variables, and both of them always greater 0, which means both e and d are changeable but the proportion of e>d>0 holds in any arbitrary scale.
Options:
a) Earthman's method is the right method.
b) Martian's method is the right method.
c) There is no one right method; therefore both methods are reasonable methods.
Please choose one of the options or add your own option, but in both cases please tell us why are you choosing or adding an option?
Thank you,
Organic
After couple of hours of communication we get this situation:
1) a not= b
Earthman: By my way (1) is a hypothesis.
Martian: 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.
Martian: 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.
Martian: 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 can a set be not completed? For example: please show us n which is not in N.
Martian: 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.
Martian: e and d are variables, and both of them always greater 0, which means both e and d are changeable but the proportion of e>d>0 holds in any arbitrary scale.
Options:
a) Earthman's method is the right method.
b) Martian's method is the right method.
c) There is no one right method; therefore both methods are reasonable methods.
Please choose one of the options or add your own option, but in both cases please tell us why are you choosing or adding an option?
Thank you,
Organic
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