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 September 20th, 2019, 10:25 AM #1 Senior Member     Joined: Oct 2013 From: Far far away Posts: 431 Thanks: 18 The discovery of zero The discovery of zero is attributed to Indian mathematicians and the often cited proof is the Bakhshali document (224 AD - 993 AD). I don't disagree. It's usually said that China had no concept of zero. However, the Chinese were first to use negative numbers (263 AD): nine chapters book. My question is very simple. How could Chinese mathematicians use negative numbers without knowing about zero? Simply put if you know less than zero how can it be that you didn't know zero? That's impossible. Perhaps someone will help me out. Thanks.
September 20th, 2019, 01:34 PM   #2
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Quote:
 Originally Posted by shunya The discovery of zero is attributed to Indian mathematicians and the often cited proof is the Bakhshali document (224 AD - 993 AD). I don't disagree. It's usually said that China had no concept of zero. However, the Chinese were first to use negative numbers (263 AD): nine chapters book. My question is very simple. How could Chinese mathematicians use negative numbers without knowing about zero? Simply put if you know less than zero how can it be that you didn't know zero? That's impossible. Perhaps someone will help me out. Thanks.

For obscure historical questions, try https://hsm.stackexchange.com/

September 20th, 2019, 02:11 PM   #3
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Quote:
 Originally Posted by shunya The discovery of zero is attributed to Indian mathematicians and the often-cited proof is the Bakhshali document (224 AD - 993 AD). I don't disagree. It's usually said that China had no concept of zero. However, the Chinese were the first to use negative numbers (263 AD): nine chapters book. My question is very simple. How could Chinese mathematicians use negative numbers without knowing about zero? Simply put if you know less than zero how can it be that you didn't know zero? That's impossible. Perhaps someone will help me out. Thanks.
You can use negative numbers without having number 0. It is a matter of concept. You can have a concept of ZERO without having number ZERO.
Like, instead of 5-5=0, you can have a statement like, "take five out of five and remains nothing."

September 21st, 2019, 01:16 AM   #4
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Quote:
 Originally Posted by shunya The discovery of zero is attributed to Indian mathematicians and the often cited proof is the Bakhshali document (224 AD - 993 AD). I don't disagree. It's usually said that China had no concept of zero. However, the Chinese were first to use negative numbers (263 AD): nine chapters book. My question is very simple. How could Chinese mathematicians use negative numbers without knowing about zero? Simply put if you know less than zero how can it be that you didn't know zero? That's impossible. Perhaps someone will help me out. Thanks.

This all stems from a very modern idea of the number line. An idea which is in fact more modern than you think. Let us actually look into some thing.

First, you know there is no year 0, right? The years go from 2 BC, 1 BC, and then immediately to 1 AD and 2 AD. Looks strange to us (even though it kind of makes sense if you think of it), but it was entirely normal to the people inventing this.

More to the point, the fact that negative numbers are smaller than positive numbers is a pretty modern invention. Even Euler had the idea that the negative numbers are in fact bigger than the positive numbers. So you'd have:
1,2,3,........ -3, -2, -1.

I have actually played with this very idea for a while in order to make some intuitive sense of the entire
$$1 + \frac{1}{2} + \frac{1}{3} + .... = -\frac{1}{12}$$
situation. Regardless, it is an idea not without merit. In the 10-adics, we have an extremely large number such as ....99999 (iinfinite digits) equaling -1, making -1 in fact the largest number in existence if we adhere to lexicographic ordering.

Did you know negative temperatures exist? I mean, negative as in below 0 Kelvin, the absolute minimum. It is interesting because those temperatures are HOTTER than positive temperatures. Noting that 0 is an impossible temperature, we would have
$$0<1<2<....<-2<-1<0$$
as in Euler's system. Temperatures exactly ARE a system where you have positive and negative temperatures, but no zero.

Of course I didn't answer your question on how the chinese dealt with this, but the acceptance of negative numbers doesn't need the concept of 0.

 September 21st, 2019, 01:58 AM #5 Senior Member   Joined: Dec 2015 From: somewhere Posts: 734 Thanks: 98 Many things works in relation with 0. Almost like complex-analysis. You can evaluate two times faster the integral of $\displaystyle e^{x}\cos(x)$ from complex-analysis. Another one is to express $\displaystyle \cos(x)$ as an infinite product, which can be done very fast ... etc. Last edited by skipjack; September 21st, 2019 at 04:49 AM.
 September 21st, 2019, 02:19 AM #6 Senior Member   Joined: Dec 2015 From: somewhere Posts: 734 Thanks: 98 $\displaystyle {\displaystyle 1+2+3+\cdots =-{\frac {1}{12}}\quad (\Re )}$.
September 21st, 2019, 08:28 AM   #7
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 Originally Posted by idontknow $\displaystyle {\displaystyle 1+2+3+\cdots =-{\frac {1}{12}}\quad (\Re )}$.
Just...no.

This is not true. Not in any context. Not even kinda sorta. Not even with caveats about analytic continuation, etc etc.

This "equation" is pure rubbish and you should not write it (unless you are writing it to poke fun at numberphile in which case, carry on)

September 21st, 2019, 08:33 AM   #8
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 Originally Posted by SDK Just...no. This is not true. Not in any context. Not even kinda sorta. Not even with caveats about analytic continuation, etc etc. This "equation" is pure rubbish and you should not write it (unless you are writing it to poke fun at numberphile in which case, carry on)
However , the sum of all positive integers cannot converge .

September 21st, 2019, 12:05 PM   #9
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 Originally Posted by Micrm@ss Did you know negative temperatures exist? I mean, negative as in below 0 Kelvin, the absolute minimum. It is interesting because those temperatures are HOTTER than positive temperatures.
I am familiar with negative pressures on the quantum scale, depending on how you define the pressure. I fail to see how you can have negative kinetic energy, however.

September 21st, 2019, 04:03 PM   #10
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Quote:
 Originally Posted by SDK (unless you are writing it to poke fun at numberphile in which case, carry on)
I think this Numberphile video on the subject has some merit.

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