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September 23rd, 2014, 08:22 AM   #51
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You are confusing the representation with the abstract object. Nobody will be able to prove that numbers are rods because they are not.

Your representation does not allow for there to be an infinite number of real numbers between any two real numbers. That doesn't mean that your representation might not have some use.

More to the point, why should someone else want to prove your fanciful ideas? You are trying to bend the mathematical world to your will. That is not the scientific method, nor is it mathematics. You must learn to listen to evidence, understand the arguments and, most importantly, be prepared to change your view when your ideas turn out to be incorrect. Mathematics is not stating results that you would like to be true, it is investigating what the rules imply must be true.

It's even fine to come up with different rules, as long as you state what they are so others can follow your logical deductions.
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September 23rd, 2014, 11:57 AM   #52
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OK everyone, it's been fun, but this thread has run its course. If anyone is interested in talking about the actual mathematics of infinitesimals, or any other related topics, feel free to open a new thread in the appropriate forum. Otherwise let's let this poor dead horse lie in peace.
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