Did calculus take it from you? 😄

@Fauxmyope2 What is the theory of zero?

@JoyfulSilence 😂. The concept of zero is entirely theoretical. Is it odd or even? How is it defined as a term in the physical sense? We spent an entire semester banging our heads until all hours of the night and it is entirely an abstract.

@Fauxmyope2 I view it from a simple counting perspective. You have a bunch of objects, like stones. One stone, two stones, three stones, etc, giving you the natural numbers. If you take one group of stones and add to it another group, then you have just defined what addition of natural numbers are. You can subtract away stones. If you take them all away, you have none left. That is zero.

Then you get into finance, assets and debts. Sometimes you owe more than you have, so you incur a debt. This is like subtracting off more stones than you have. The debt is like the negative numbers. If you offset the debt with an equal sized asset, you have zero debt and zero assets. A number plus its negative is zero!

So now you have the integers. This is an example of a additive "group". Zero is the additive identity of that group. It means when you add anything to zero you get back what you started with.

Then you start multiplying stones together. You make groups of groups, rows times columns. Then you divide. All the ways you can do so is defined by all the possible shaped rectangular arrays of stones you can make. This gives you a "ring" of integers (with addition, subtraction, and multiplication).

Then you have pies that you divide up into fractions, and all the rules of arithmetic for fractions. You add integers to them, and get rational numbers. Multiplication/division is its own algebraic group. The number 1 is the multiplicative identity. So this ring is actually a "field" (when the multiplicative operator induces a group).

Then you start taking roots. What is the square root of -1? Who cares. Just call it "i" and then use it as a variable and do algebra, yet make sure that its square is always -1. So you have complex numbers over the field of rationals.

Then you play with number lines, and ask about the spaces in between. You look at infinite sequences of rational numbers, and their limits. And roots of rational numbers that are not rational. So you have irrational numbers. The combination gives you the real numbers. Include i, and you have the complex numbers. Etc.

@JoyfulSilence That is how I interpreted zero before and after the course. During the course, it was a demonic plague.

@Fauxmyope2 Sounds like a fun course!

@JoyfulSilence. I never took another math course.

@Fauxmyope2 I got an MS in math. Then got hired as a statistician and had to take more courses since I did not study statistics that much in school. I am still learning! And techniques change. Some things that were too impractical years ago are easier now due to increased computing power. Sometimes it is easier to just try a bunch of possibilities, do some simulations, apply some models, than try and find some perfect algebraic solution.

Yet I still push he envelope. My last program was going to take 300 hours to run so I split it into 13 smaller programs and ran them simultaneously and let the Linux server handle it all as they all vied for the CPUs and memory.

@Fauxmyope2 I hear you lol Zero seems more in the realm of Philosophy than that of Pure Maths.