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Topic: Cumulative MatheRealism Report 15.05.14
Replies: 0

 JÃÂ¼rgen R. Posts: 1,085 Registered: 12/13/04
Cumulative MatheRealism Report 15.05.14
Posted: May 15, 2014 7:37 AM

The Perfosser is not producing much new material.
His current plan seems to be to exhaust the enemy by repetition
of tedious apparent fallacies in order to launch a surprise attack
with brilliant new insights at the appropriate time.

In MatheRealism there will not only be an entirely new theory of the
infinitesimal calculus, but also some new laws of arithmetic, such
as No. 42 and 41.

42. If z = x + iy and x = 0 then z^2 = x^2 + y^2,
thus (iy)^2 = y^2 and 1 = -1.

41. If z = x + iy and x = y then z^2 = x^2 + y^2,
thus (1+i)^2 = 2, 2i = 2 and i = 1.

40. Since the anti-diagonal cannot have more digits than every entry up to
its digit a_nn
at the finite place n, the anti-diagonal cannot be distinguished from
infinitely
many rationals too. Not having seen this obvious fact will embarrass
thousands of matheologians

39. The notion of finished infinity implies the truth of P and not P.

38. An algorithm is not confined to a finite number of steps

37. Theorem of non-exhaustibility (Mückenheim 2014):
We always can "prove" that for every natural number there are much more
than 1/epsilon := M rational numbers. Since you can pair one rational,
for instance 1/p^n (with p a prime number) with one natural, for instance n,
the rationals will *never* be exhausted in this way.
And why should we not do this pairing? Have you ever wondered why?
Because the rationals will never become exhausted!
Hallelujah!

36. "Countable" is nonsense!
But if it was (sic) meaningful, then the set of reals was (sic) countable.

35. "Countable" is not a notion of mathematics

34. A real number cannot be sufficiently given by digits unless all digits
are given.
Otherwise the number is not defined.

33. There is no definition of definition. But every known real number has a
definition.
Therefore there cannot be more than countably many real numbers

32. Infinite sets do not exist.

31. The amount of information in the universe places a limit on the possible
contents of mathematics, namely at most 10^80 imperial gallons.

30. Although all available numbers have a finite contents of information,
there is not a greatest number, because, by useful abbreviations,
numbers as large as desired can be represented by means of little
information.
(The Perpetuum Mobile of MatheRealism)

29. In Germany we have not yet sunk to the US-level of scientific education

28. The decision to accept undefinable numbers does not change anything in
mathematics

27. f(t + T) = f(t) is equivalent to f(x + 2pi) = f(x) for any T

Matheology.

2. All proofs of the existence of uncountable sets are wrong.

3. Countability is a valid concept in MatheRealism when the "frame" is
appropriate.

4. Infinity is always potential, never actual, though neither countable
nor uncountable.

5. Cantor caused "disaster to overtake mathematics".

6. 0.111111.... is an abbreviation for 1/9, it is the limit of the
implied partial sums

7. It is not possible to list infinite sequences. Irrationals cannot be
defined by their digits.

8. If {S_n} is a sequence of sets lim Card(S_n) = Card(lim S_n)

9. Every solution that exists can be identified and can be expressed

10. Set theory is self-contradictory, but this has no effect on the
results of "Mathematics"

11. Every digit belongs to infinitely many rational numbers

12. All elements of mathematical discourse belong to a countable set

13. Set theory is abolished

14. Every expression defines (or points to) itself and probably to some
other objects.

15. Every finite expression and every subset of finite expressions is
its own definition

16. A list is countable. An alphabet is linearly ordered, i.e., not only
well-ordered. But uncountable sets cannot be linearly ordered.

17.It would yield nonsense if a function "at infinity" had really
any value other than zero.

18. If a set is the union of countably many subsets it has no further
subsets,
because no elements are available to distinguish these (Principle of the
Binary Tree).

19. Elements of a countable set cannot make an uncountable set.

20. For every string that does not yet point to a real number like sqrt(7),
we can find a real number which this string points to like sqrt(8).
Iinfinitely many occur infinitely often.

21. Infinite expressions do not define anything because they have not a last
letter,
but every other letter is followed by infinitely many further letters.

22.To claim undefinable Dedekind-cuts is an insult to Dedekind

23. The list of defined real numbers has an infinite diagonal.
But infinite diagonals like infinite strings of digits do not define
anything.

24. Why are the real numbers countable? Because they are not defineable by
infinite strings of digits

25. Mathematics is defined by "all that, which can appear in mathematical
discourse, dialogue or monologue"

26. numbers like (10^10^10^10^10)!!!!!! belong to the smallest in
MatheRealism and there is no greatest number known