In the thread "0.99999~ = 1 ?" (
Message 1), talk has turned somewhat to a topic slightly different from that first introduced and proposed. Specifically, the issue at point is no longer the distinctness of two numbers, but the foundations of the entire system of Mathematics (what I called MATHSYSTEM) in relation to the real world (what I called REALWORLDSYSTEM).
As I stated in
Message 87
... more a matter of definition than a matter of real-world fact.
A consequence of some proofs in
Message 110:
P "All #s with property Z are REAL within MATHSYSTEM (i.e., ((R/Z)/M) (M=MATHSYSTEM)"
P "0.9999| has property Z"
P "(The REAL of 0.9999| is True) given MATHSYSTEM is True (i.e., ((R/0.9999|)/M))"
P "[proof of M=True]"
C "(R (the REAL of 0.9999|) is True... period"
Proof that .9999| is not DISTINCT (from 1):
P "It is false that 0.9999| is both REAL and DISTINCT (from 1) (~(RD))"
P "(R (the REAL of 0.9999|) is True... period"
C "0.9999| is not DISTINCT (from 1)"
... which was a consequence of the proofs explained in
Message 89:
Proof that .9999| is REAL:
P [P1 for .9999| being a REAL number]
P [P2 for .9999| being a REAL number]
etc.
C [Conclusion that .9999| is a REAL number]
Proof that .9999| is not DISTINCT (from 1):
P1 "It is true that 0.9999| is REAL"
P2 "It is true that 0.9999| is DISTINCT (from 1)"
P3 "It is false that both P1 and P2 are true (~(P1P2))"
P4 "[conclusion from proof of 0.9999| being a REAL number], i.e., P1 is true"
C "P2 is false, i.e., .9999| is not DISTINCT (from 1)"
... along with the definition of REAL I had been given as being ultimately dependent on the MATHSYSTEM (see posts in reply to me, especially by Dr. A.), and as RAZD concurred in
Message 117:
RAZD writes:
math does not need to conform to reality
... the MATHSYSTEM appears to have no necessary relationship to the REALWORLDSYSTEM. As was shown in my reply to Dr. A, which was
Message 120:
1 = 3/3 = 1/3 + 2/3 = 0.3333| + 0.6666| = 0.9999| ≠ 1
So, the MATHSYSTEM introduces a function that equates 0.9999| with 1 and thereby closes the paradoxical loophole, such that we may continue using the MATHSYSTEM as a representation of the REALWORLDSYSTEM. Of course, just because we can mend one system so that it will represent another, does not indicate a necessary representative property of the former system in regards the latter, i.e., it does not show that the former system represents by necessity the latter system, but merely shows that it represents it, not necessarily by necessity.
Afterall, any system that represented necessarily another system would not need a function to close paradoxical loopholes, as such loopholes would not exist. The fact that the MATHSYSTEM has introduced such a function in an attempt to represent the REALWORLDSYSTEM, shows that the MATHSYSTEM is not necessarily representative of the REALWORLDSYSTEM.
... were there a necessary relationship between the MATHSYSTEM and the REALWORLDSYSTEM, they would both paradoxically collapse in upon themselvesI mean, the paradox related to their existences would cause them to cease existing.
In
Message 123, Rrhain writes in response to my question whether there is any reality in the real numbers:
Rrhain writes:
That is a philosophical question, not a mathematical one. You are playing to the distinction between Platonists and non-Platonists.
And that, to most mathematicians:
... the objects that mathematics studies are real.
So, I would like to challenge any mathematicians who hold this view to support such. I am not convinced that the MATHSYSTEM is necessarily linked to the reality that it describes. As I pointed out in
Message 120, certain internal operators of the MATHSYSTEM which function to tweak its failures to match the REALWORLDSYSTEM so it can be a better describer are part of the evidence I will offer initially that the MATHSYSTEM could not be a necessary representative of the REALWORLDSYSTEM, i.e., it does not represent it by necessity, but rather by convention. Or, in the words of Rrhain, I'm going to pull a Bert.
Jon
Edited by Jon, : No reason given.
[O]ur tiny half-kilogram rock just compeltely fucked up our starship. - Rahvin
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