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Philocrat
Philocrat is offline
#3
Jun4-05, 08:34 AM
P: 579
Quote Quote by Sabine
x= 0.99999....

10x = 9.999999.....
10x= 9+ 0.99999.....
10x-x = 9
9x=9
x=1

=====> 1= 0.99999....

is there smthg wrong?
Mathematicians (and paherps those in quantitative disciplines too) might not have problems with these mathematical propositions that you are invoking, but I can assure you that philosophers would definitely have serious problems with them. For a start, metaphyisicians, epistologists, Logicians, language philosophers, and philosophers in the philosophy of science discipline would be outraged by these sort of m-propositions.

Perhaps, if they feel like being generous, they would accept them as approximations. But in a hard-headed mode of philosophysical analysis, such approximations would not pass for sound and conclusive mathematical truths.

Infact, leaving philosophers aside, in the real world such m-propositions would not stand a chance. Simply, it would be practically unaceptable in many practical circumstances or situations. For example, take a peny out of ten pounds (10) and what results is 9.99. Without wandering too far to draw a concret example, I have personally encountered several instances where the shopkeeeper resfused to accept a price with a missing penny (ie refused to accept 9.99 for a 10 price.) Practically, it seems that these shopkeepers refused because of the missing penny (0.01). Also, if you take a penny out of one million pounds you are no longer a millionaire for a very obvious practical reason (1,000,000 - 0.01 = 999,999.99).

IMPORTANT POINT

Mathematicians must keep 'Absolute Truths' separate from 'Natural Approximations'. They are two fundamentally different things. Philosophers, especially those in the above listed disciplines, rigorously enforce this distinction. The world where we can avoid fractions and the usual associated vagueness is currently a distanced dream, if not completely an impossiblity. I have suggested elsehwere on this PF the need to start looking at the "MATHEMATICS OF 'THE PERFECT FIT'" that governs a 'paraplexed world or universe'.