The art of mathematical argument

BidenPresident said:
Structure.
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Like this?

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The Ramanujan Summation: 1 + 2 + 3 + ⋯ + ∞ = -1/12?

“What on earth are you talking about? There’s no way that’s true!” — My mom

This is what my mom said to me when I told her about this little mathematical anomaly. And it is just that, an anomaly. After all, it defies basic logic. How could adding positive numbers equal not only a negative, but a negative fraction? What the frac?

https://www.cantorsparadise.com/the-ramanujan-summation-1-2-3-1-12-a8cc23dea793


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Cypress said:
Mathematical proofs are the gold standard of knowledge.

Once a mathematical statement has been proved with a rigorous argument, it counts as true throughout the universe and for all time.

The experience is the closest you can get to glimpsing the abstract order behind all things.


Notable mathematical proofs

The square root of 2: Can the square root of 2 be expressed as a rational number—that is, as a fraction of two integers? The discovery by the ancient Greeks that square root of two is an irrational number was considered so dangerous, that the geometer Hippasus was murdered to prevent the knowledge from being disclosed.

Geometric series: Is the repeating decimal 0.99999… less than 1? Or does it equal 1? The proof that 0.9999... is actually equal to 1 surprises many people and provides a launching point into the analysis of infinite geometric series in calculus.

Countably infinite sets: An eye-opening proof shows the counter intuitive notion that the set of all rational numbers is the same size as the set of all positive integers, even though there are infinitely many rational numbers between two consecutive integers.



Insipration and credit: Professor Bruce Edwards, University of Florida
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Not everything is mathematical.

My choice to drink Coca Cola is not based on math.
But on desire.
 
BidenPresident said:
No.
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I have never seen any definition like yours that says all meaningful information is code. A definition like that is so overly broad as to be useless.

I have never heard art, photography, music called code in any conventional way people normally talk.

Everything I listed has underlying mathematical principles, they do not require your consent to confirm it.

All electromagnetic radiation has frequently, wavelength, periodicity. All music is based on the mathmatics of harmonics. All photography is based on the principles of optics, apeture, focal length, digital pixelation. Artistic compositions routinely employ the mathmatics of linear perspective, foreshortening, and the golden ratio.
 
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