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-   -   How does math deal with the history of numbers? (http://mymathforum.com/number-theory/344521-how-does-math-deal-history-numbers.html)

justintimmer July 5th, 2018 07:39 AM

How does math deal with the history of numbers?
 
How does math deal with the history of numbers? Suppose you have 70 euros and lose 30 euro. While someone else has 10 euros and gains 30 euro. In math, this would state 70-30=10+30, and you are allowed to change this to 40=40. The both sides would be equal, but they are not equal, because they have a different history and probably will feel different with having 40 euro. So should you be allowed to change 70-30=10+30 to 40=40?

I know I make this example quite weird by adding some subjectivity into it. But I hope you get the drift. I am no mathematician, and I am not really sure whether I post this question in the right topic.

greg1313 July 5th, 2018 10:39 AM

You need another system; an accounting system for example. Two 2's make 4, regardless of where the 2's come from.

skipjack July 5th, 2018 10:44 AM

Obviously, 70-30 and 10+30 are different expressions, but they have the same numerical value.

Maschke July 5th, 2018 11:09 AM

https://en.wikipedia.org/wiki/Bookkeeping

JeffM1 July 5th, 2018 05:50 PM

Quote:

Originally Posted by justintimmer (Post 596241)
How does math deal with the history of numbers? Suppose you have 70 euro's and lose 30 euro. While someone else has 10 euro's and gains 30 euro. In math this would state; 70-30=10+30, and you are allowed to change this to 40=40. The both sides would be equal, but they are not equal, because they have a different history and probably will feel different with having 40 euro. So should you be allowed to change 70-30=10+30 to 40=40?

I know I make this example quite weird by adding some subjectivity into it. But I hope you get the drift. I am no mathematician, and I am not really sure whether I post this question in the right topic.

You need to study utility theory. If I have 100 million dollars and lose 1 million dollars, I have 99 million dollars, but the "utility" that I have lost may be minor. if I have nothing and win 99 million dollars, I have 99 million dollars, but the "utility" that I have gained may be immemse. In both cases, my final monetary situation is the same, but, psychologically, my reactions may be very different. "Utility" need not be (and empirically almost certainly is not) linear with respect to money.

This has nothing to do with math and all to do with human psychology.

EDIT: This is what marginalsm in economics is all about. A monetray gain of x and a monetary loss of x seldom have the same emotional and psychological weight.

Country Boy July 7th, 2018 04:17 PM

Quote:

Originally Posted by justintimmer (Post 596241)
How does math deal with the history of numbers? Suppose you have 70 euro's and lose 30 euro. While someone else has 10 euro's and gains 30 euro. In math this would state; 70-30=10+30, and you are allowed to change this to 40=40. The both sides would be equal, but they are not equal, because they have a different history and probably will feel different with having 40 euro.

You seem to have difficulty with the definition of "=". When you say "they are not equal, because ..." you are using a different, non-mathematical meaning of "equal".

Quote:

So should you be allowed to change 70-30=10+30 to 40=40?

I know I make this example quite weird by adding some subjectivity into it. But I hope you get the drift. I am no mathematician, and I am not really sure whether I post this question in the right topic.


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