[–] oneunderall 2 points -1 points 1 point (+1|-2) ago
What is this dumb shit? Are you serious with this thread?
I need to browse more topics in this sub to get a better idea of what level math you guys are at. I can post way better shit than this just off the top of my head.
[–] VIP740 0 points 2 points 2 points (+2|-0) ago
Then, my noble friend, geometry will draw the mind towards truth, and create the spirit of philosophy, and raise up that which is now sadly allowed to fall down. -Plato
Can zero become an obstacle? Odd as it may sound there have been times when zero stood in the way of mathematicians, and they had to develop some fairly sophisticated tools to get around it.
To the Greeks math was foundation of philosophy. Upon Plato's academy was said to be the sign "Let no-one without knowledge of geometry enter". Philosophers such as Plato and Zeno saw our world as an illusion, and math as the truth. By studying mathematics they would free themselves from the falsehoods which bind us to this world of imperfections.
Can you draw a perfect circle? Imperfections can be found even in the best painter's work if enough scrutiny is applied. But the mathematician should be able to create one through pure logic. Now we are taught the formulas C = 2πr, and A=πr2 in grade school, but most aren't taught where they came from. Before these could be taught, someone had to figure them out, history names this person as Archimedes. The visualizations @plankO shared with us will cast some light on the mathematics involved.
It's easy to see the area of a rectangle is given by the base by the hight. Cut it into triangles and you'll see all triangles have half the area of their base times height. This lets you measure the area of any polygon, as they can all be divided into triangles.
But a circle isn't a polygon. We can approximate circles from polygons, but the Greeks demanded perfection. While we could think of a circle as a polygon with infinite sides, the Greeks saw infinity as representing incompletion. Besides, the area of each triangle would get smaller and smaller, if you never stop cutting your figure into smaller triangles, can there be anything left when you get done?
I started with six triangles forming a hexagon, then cut it up into twelve smaller triangles forming a dodecagon. And I kept cutting my figure closer to the form of a circle until there was nothing left to cut. Thus I discovered the area of a circle to be 0 * ∞.
The Greeks would view this as complete nonsense. We could use this argument to make anything we want to represent 0 * ∞, it would be worthless as a formula, giving us no details distinguishing one thing from another. Archimedes found a way around this problem. He said no matter how many sides you give the regular polygon you inscribe inside the circle, it will always have less area than the circle enclosing it.
This doesn't give us a perfect measure, but you could also place a larger polygon "hugging" the circle (so that the middle of each side rather than the corners touched the circle). So the area of the circle is greater than any regular polygon which could be inscribed inside of it, and less than any regular polygon that could be built around it. Archimedes used this idea to come up with his formula for a perfect circle without having to worry about zero or infinity. His method reveals how closely the mathematics of circles and triangles are tied.
Newton and Leibniz came up with a more general way to get around the problems zero could cause. While calculus served as a great tool for scientists, philosophers were skeptical of Newton's vanishing quantities and the infinitesimals of Leibniz. So to solidify the reputation of calculus, mathematicians such as Weierstrass set out to banish unclear ideas such as infinities from the science. They went through calculus, and when they found statements like this:
...the ultimate ratio of evanescent quantities is to be understood the ratio of the quantities not before they vanish, nor afterwards, but with which they vanish.
They replaced them with statements like this:
Let f be a function defined at all points near x0, except perhaps at x0 itself, and let l be a real number. We say that l is the limit of f(x) as x approaches x0 if, for every positive number ε, there is a positive number δ such that |f(x)-l| < ε whenever |x-x0| < δ and x ≠ x0. We write lim x->x0 f(x)=l.
Now we don't have to worry about infinities or division by zero. Even if the details are hard to follow, we do at least have the details. No longer will zero and the ambiguity surrounding it stand in our way. Many thought infinity had been laid to rest at this point, but a student of Weierstrass brought it back into modern mathematics, rekindling some ancient debates.
[–] TheBuddha [S] 0 points 1 point 1 point (+1|-0) ago
pondering
I'm so going to cop out and day that any mathematical concept can be a an obstacle. For instance, we have those who think linear math allows division by zero, concepts such as infinity breaking basic maths, and things like Zeno's paradoxes (such as Achilles and the tortuous) that we work around.
Yeah, I'm so taking the low road with this answer. ;-)
[–] TheBuddha [S] 0 points 2 points 2 points (+2|-0) ago
The history section of this page may interest you.
https://en.wikipedia.org/wiki/0
Everyone else, we see the number increase so we know people looked.
Jump in! Question, ask, opine, offer correction, insight, or whatever. Don't worry about being wrong. Just dive in. The water is warm!
I think that's cause someone pissed in it, but it's warm!
[–] Opieswife 0 points 2 points 2 points (+2|-0) ago (edited ago)
Ok this was interesting. I haven't really thought about this before but I totally get what the author is trying to say. At first I wasn't sure where he was going but at the end it came together. Looks like I have more reading to do. :)
[–] VIP740 0 points 2 points 2 points (+2|-0) ago
I don't remember when I first came across the distinction, but I do remember the first time I tried to explain it to someone else. It went something like this:
Well zero isn't exactly the same thing as nothing. If you have a graph of y=mx+b there's a point on there where y=0. But with nothing... err, um...
Yeah, I get what you mean, it's not nothing, it's zero. If you have nothing... (scratches head).
[–] [deleted] 0 points 2 points 2 points (+2|-0) ago
See? Zero is all over the place!
Anyone else have any Zeros that they run into?
For the night, I'm mostly going to be over here:
https://voat.co/v/guitar/2248107
Music is math. So, I'm dropping some music tonight. ;-)
[–] TheBuddha [S] 0 points 1 point 1 point (+1|-0) ago
The rules of mathematics impose limits. For this, we get my favorite example of the infinitesimal nines equalling one. But, also because of this, most of the math folks think that 0^0 = 1. On tablet, not doing fancy notation.
Which is, of course, absurd. Calculus textbooks usually say it is undefined and wash their hands of the subject, and that's probably the smartest thing to do. However, in about 1994(?), someone provided proof that it equaled 1. This, of course, didn't actually end the debate. Last I knew, someone had posited a rebuttal and it was an obscene 100+ pages long. The difficulty being that they had to now prove no such thing was true.
I usually stick with it is undefined because, seriously, they are really contrived at this point. Like infinity and randomness, these very thoughts lead to insanity.
[–] TheBuddha [S] 0 points 4 points 4 points (+4|-0) ago
https://medium.com/@howdypierce/negative-zero-bbd5fd790af3
[–] VIP740 0 points 2 points 2 points (+2|-0) ago
Interesting. I guess that would explain some things about this article, as it's geared toward software developers. Thanks for finding that.
[–] TheBuddha [S] 0 points 2 points 2 points (+2|-0) ago
Maybe, I'm still not strictly sure what he's on about. That's what prompted me to do more looking.
[–] Opieswife ago
So I feel like this would make more sense but I am missing a fundamental or two. Can you help so I can reread this again and hopefully make sense of it. I think I am close...
Ok what does floating mean? That you can move essentially on a number like between both positive and negative numbers? Both to what I visualize is to the left and right if zero? Or does this mean something completely different?
Next question I have not seen a double sign before. I don't know how to make it on my keyboard but I am talking about the plus over the mibus sign before the 0.0. Does that mean the 0.0 or whatever number follows can be either positive or negative?
Thanks once I know what these mean I will try reading again and see if I can get further and make more sense out of this.
[–] TheBuddha [S] 0 points 1 point 1 point (+1|-0) ago
Well, we're going to have to start back at what are numbers and work our way out from there! ;-)
I can do that - but it might be slow. I'm going to do a music dump in the guitar sub. But, here's a link to get you started. When you get that, just say so.
http://web.mst.edu/~kosbar/test/ff/elem/typesofnumbers.html
If you'd rather listen to music:
https://voat.co/v/guitar/2248107
(I'm an accomplished musician, my background is in classical guitar but began with percussion instruments. Playing in a band helped me provide extra money.)
[–] VIP740 0 points 1 point 1 point (+1|-0) ago
LOL! OK so the computer represents everything with ones and zeros. You have ASCII characters like 'A'=01000001, and '0'=00110000. It's easy to represent positive integers. So in one byte we could store 256 values, which could be interpreted as 0 - 255: 00000000, 00000001, 00000010, 00000011, 00000100... But what if we need to store negative numbers? Well if we add one to 255 (11111111), each digit carries over, leaving eight zeros and a carry that flies off into never never land. So 11111111 can be interpreted as 255, or -1. To change the sign of a binary number you can first not each bit (change zeros to ones and ones to zeroes), and add 1 to the result. Floating point numbers can have fractional values. It's called floating point because we have a section of bits that changes the location of the decimal. Lets say we have four digits and a point to represent a decimal number, like 4329. We could change the size of our numbers by moving the decimal: 4329, 432.9, 43.29, 4.329, .4329. The computer does something like that in binary. The position of the point is determined by the first few bits, and the other bits are interpreted as being multiplied by that power of 2.