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A Game of Numbers


Starlord

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Zero is the additive identity.  Adding zero to any number results in that other number, unchanged.  Multiplication is just repeated addition.  An infinite number of added zeros retains the original number, and if that itself was zero, then you still have zero.

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8 hours ago, Cancer said:

Zero is the additive identity.  Adding zero to any number results in that other number, unchanged.  Multiplication is just repeated addition.  An infinite number of added zeros retains the original number, and if that itself was zero, then you still have zero.

Cheers

 

The approximate argument that zero is not a number:

One school of thought, states that quantity is a derived property of a thing. The representation of quantity is our numerical units. Units being "of unity" ie one. If this is the case, then zero can't be a number because it hasn't a thing to give it its quantity -- a subtractive emptiness is nothingness or non-existence. The counter argument would be: there was something here, now there is nothing here. This  "nothing here" is represented by zero. The issue then is can you represent ten as Unity additive to Nothing-here? 

 

Looking at this*, the Egyptians had a good point: a new symbol to represent ten, hundred etc. A specific symbol shows the positive existence of the quantity represented. *https://mathshistory.st-andrews.ac.uk/HistTopics/Egyptian_numerals/ 

 

Disclaimer: of course being a Westerner, I'm used to zero and the number system we have and given ten symbols can represent an indeterminate repetition of numbers.

 

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The Origin of Zero - https://www.scientificamerican.com/article/history-of-zero/

 

A Brief History of Infinity - https://www.scientificamerican.com/article/a-brief-history-of-infinity/

 

Does Infinity Really Exist? - https://www.scientificamerican.com/article/does-infinity-really-exist/

 

Dispute over Infinity Divides Mathematicians - https://www.scientificamerican.com/article/infinity-logic-law/ or https://www.quantamagazine.org/to-settle-infinity-question-a-new-law-of-mathematics-20131126/

 

How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer.- https://www.quantamagazine.org/how-many-numbers-exist-infinity-proof-moves-math-closer-to-an-answer-20210715/

 

Mathematicians Measure Infinities, and Find They're Equal - https://www.scientificamerican.com/article/mathematicians-measure-infinities-and-find-theyre-equal/ or https://www.scientificamerican.com/article/mathematicians-measure-infinities-and-find-theyre-equal/

 

Is Infinity Real? - https://www.quantamagazine.org/the-infinity-puzzle-20160616/

Solution: ‘Is Infinity Real?’ - https://www.quantamagazine.org/the-infinity-puzzle-solution-20160630/

 

How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer. - https://www.quantamagazine.org/how-many-numbers-exist-infinity-proof-moves-math-closer-to-an-answer-20210715/

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