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- Understanding the intuition behind math 4 answers
This question explains better what this one tried: Understanding the intuition behind math
In the history mathematics we always see how the numbers were created and for what purpose. Like ordering, calculation of areas and taxes. This is the most common approach on documentaries and so in the math books.
It's always easy to understand the basics: Add, subtract, multiply and divide. The reason it is easy is that it is intuitive. We can imagine those things happening in our minds through visual representations.
I'm digging these documentaries looking for the part where we jumped from these basic operations to the complex ones. At least to me, the complexity starts when we add negative numbers. For example, in this simple operation:
$1 + (-1) = 0$
It's easy to understand how to apply and use the provided logic of signs. But to me it is not easy to imagine what is really happening here. And when I say "happening", I mean that I can't create any object visualization of that operations, like the ones we learn on high school:
"Imagine that you have two breads. You have eat one. Now how many do you have?"
On that kind of visualization you can imagine the two objects and then you can take off one and see how it looks like. This can be done for all the basic four operations on small scales.
You could say that the operation above is the same as $1 - 1 = 0$ But that's not the case. Doing so you are omitting the signs part and using it just as predefined formula.
The main question is about when in the history and for what reason the man came out with the signs and that kind of operation. In other words: Which was the first step given after these basic and very intuitive operations? And which was the necessities that leverage these discoveries? Like the need to have a convention where plus and minus become minus.
It is easy to think of debts. In that case, can you provide a simple visualization like the mentioned above for the product of two negative numbers?