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Originally Posted by Renk
the MIT paper to which I gave a link above (that you haven't studied, or even read)
if not, show me where are the errors in the paper I gave to you
why would i bother reading such nonsense? to see how math can be used and abused?
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because mathematically you can duplicate an object in 2 other objects each having the same volume as the former, which seems to be impossible in the physical world (reason why achieving something like this is considered as a miracle)
linguistically you can invent words without meaningful physical counterparts
artistically you can display things normally impossible in the physical world
philosophically you can establish imaginary concepts
historically you can invent false events
theoretically you can support erroneous concepts
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showing that obviousness and "common sense" are not criteria of mathematical truth. Something can be mathematically true and completely defying common sense in the same time.
on the contrary, in order to apply mathematical expressions properly, their usage and meaning needs to be understood: obviousness and common sense is certainly needed
improper usage may lead to paradoxes
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maybe by manipulating what physicist name nowadays dark matter and black energy)
dark matter and dark energy are imaginary scientific concepts used as a crutch to support their flawed theories, as in: 'we are missing something in our calculations... lets call it the dark energy'
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tell me what exactly is the political content (leftist? rightist? centrist?) of the following assertions:
mathematical models can be written in such a way to support a certain political agenda, even though the mathematical expressions used therein are politically neutral
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In fact, what you qualify as "logical" is only what your common sense considers as true. But by doing so, you make yourself deaf and blind to any radical novelty and you make it impossible for you to make any evolutionary leap. Just because something shocks your intuition or threatens the way you view and comprehend the world doesn't mean that this something is illogical or false. And just because you don't take the trouble to study a theorem that defies what you call common sense, doesn't mean this theorem is false either.
that is exactly the problem with mathematics (or mathematicians) nowadays: they are often divorced from logic and reality, playing like children, building their imaginary castles in the air, which is simply a sign of the times in the age of ignorance
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In fact, you are contradicting yourself: First you refuse to accept the fact that 0.999...=1 only because this assertion is not compatible with what you name common sense and logic, ultimately leading you to then have to admit the existence of a "number" that can't be divided by any other number than 1 and itself, and to admit the existence of an interval that has no middle point, what completely defies obviousness and common sense as well...
on the contrary, i have already shown on multiple occasions that 0.999 does not equal 1, be it mathematically or logically - seems to me you are the one constantly trying to find some way to support this idea
what i did there is pointing out how generally by abusing mathematics no concept is safe from ending up perverted and how any perversion can be accepted as valid these days
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1) What is the smallest positive number divisible by 10 (let name it r)? How do you write it? What is the decimal representation of this number?
2) Now let consider your d. What is the decimal representations of 10*d?
this was already answered before:
1*d = 0.0...1 <> 0
...
10*d = 0.0...10 <> 0 - this one has (n-1) leading zeroes, it is 10 times larger than d
100*d = 0.0...100 <> 0 - this one has (n-2) leading zeroes, it is 100 times larger than d
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what are the nth digits of these numbers?
in every one of these numbers: all digits are 0, except for one of them, which equals 1