0
0

[–] TheBuddha [S] ago 

This is good, I've moved it to sticky. Unsticky it when you're done?

0
1

[–] VIP740 0 points 1 point (+1|-0) ago 

What are everyone's thoughts on 00?

0
1

[–] TheBuddha [S] 0 points 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.

0
0

[–] VIP740 ago 

0
0

[–] TheBuddha [S] ago 

0
2

[–] VIP740 0 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.

0
1

[–] TheBuddha [S] 0 points 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. ;-)

0
0

[–] VIP740 ago 

I'm so going to cop out and day that any mathematical concept can be a an obstacle.

Did the spell-checker fix deny for you? Obstacles or not, there's definitely some confusion and frustration in the study of mathematics.

0
1

[–] TheBuddha [S] 0 points 1 point (+1|-0) ago 

2
-1

[–] oneunderall 2 points -1 points (+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.

0
1

[–] Opieswife 0 points 1 point (+1|-0) ago 

Don't cop an attitude, just post or start another subverse that is more to your liking.

0
2

[–] TheBuddha [S] 0 points 2 points (+2|-0) ago 

Well, get posting.

Why this? Because my goal is to make it at a level anyone can appreciate.

0
2

[–] Opieswife 0 points 2 points (+2|-0) ago 

Your doing great. I love that you smart guys are posting and taking time to answer my questions. I wish I had someone like you or @VIP740 as an instructor when I was on school. You both make math interesting.

0
2

[–] 11109140? 0 points 2 points (+2|-0) ago 

Zero is where all real arrays start. Same with any enumerations. So if you want the last item in the list you have to do List(List.Count - 1).

0
0

[–] TheBuddha [S] ago 

Another use for 0!

[–] [deleted] 0 points 1 point (+1|-0) ago 

[Deleted]

0
0

[–] TheBuddha [S] ago 

load more comments ▼ (3 remaining)