My Math Forum A Number is a Value or a Measure ?

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July 3rd, 2017, 12:33 PM   #21
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 Originally Posted by Maschke I agree with your point. I think we need a philosopher of physics to explain why counting is exact but measurement isn't. My remark holds if we distinguish measurement from counting. For example the number of coins is exact but their weight can never be exact.
Actually physical counts are frequently inexact, and for the same reason that physical measurements are inexact: the device doing the counting is not perfect in a Platonic sense.

Many years ago I had a summer job in a warehouse and had to check inventory records. It was not unheard of for me to count say 17, look down at the inventory and see 16, which was a correction from the previous inventory count of 17.

The difference, I think, is that counting repeatedly will usually come up with identical results.

July 3rd, 2017, 12:50 PM   #22
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 Originally Posted by JeffM1 Actually physical counts are frequently inexact, and for the same reason that physical measurements are inexact: the device doing the counting is not perfect in a Platonic sense. Many years ago I had a summer job in a warehouse and had to check inventory records. It was not unheard of for me to count say 17, look down at the inventory and see 16, which was a correction from the previous inventory count of 17. The difference, I think, is that counting repeatedly will usually come up with identical results.
Very good point. The 2000 Gore v. Bush election showed that we can't actually count very well when the numbers get large. We can count perfectly to 3 or 4, but not to 100 million. In the latter case, we are bound to make errors.

July 3rd, 2017, 10:24 PM   #23
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 Originally Posted by Maschke Are you saying you understand advanced algebraic geometry, category theory, schemes, and all of that? Are you making that claim? Or what exactly was your reference to Grothendieck all about?
In read and speak French, but not hahdy hieroglyphs... So I can just read what is translated in a typo pdf... So at the moment I will say you I'll be happy once I'll be able to read him (understanding is very far... still if some new concept is very close to mine) ;-P

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