Math Is Fun Forum

So do you believe in zodiac?

It's like somebody behind you just push you, and you push someone in front of you, and they are not the same push.

Well, I think that may largely lies in transition of knowledge, that when you have a concept, it is similar to a concept you've learned. My instance: determining how many digits of a product in Help section, I unconciously borrow the sandwich theorem in calculus.

In common reasoning, one will think step by step, having little chance to get a leap of reasoning all of a sudden. And if so, I guess it will be sheer guess.

What about your experiences? May you analyze them, and see if my hypothesis stands.

However, you can try parametric plotting, such as (5cos(t), 5sin(t)), where cos(t) and sin(t) are well defined as functions.

And what do you mean by infinite series? Can I think of it having infinite entries? So what does "infinite" stand for when you deny infinity as a number?

"Integrals are done on the assumption that there are no infinitesimals."
-The sum will never reach the amount to which the limit approaches unless the pieces being divided into full-developed infinitesimals.

"0 is not an integer?"
-First, having to be Integers but not all of them. When applying integers, you are not dellusioned to foolishly devide an amount by 0, and you know perfectly the denominater is an integer Except 0. But common economic books give a continueous curve to plot the function, with "AVC" beside vertical lines on the left, which is definately misguiding. If a discrete step by step, no one will make that mistake.

"closing" basis?
yes, N-∈ or Delta-∈ defination by Cauchy, which does not state "reaching" in any conditions.
Besides, do you know where epsilon comes from? One book I've read say it is from the ancient greek word " error".

"We can not infinitely measure anything.  Thus, any statements about the exactness of the universe is pure speculation and nothing but."
-Actually infinity concept is fundamentally flawed proven by simple reasoning and have no reason to exist, which I shall illustrate later.

Yeah, I know that- anything relating to limit have something to do with this defination, derivatives-tangents, magnitudes(with nabla notations),and all kinds of integrals.

But the defination only assume their accuracies instead of their more-or-less nature. I bet a electrodynamic professor will advice you to use integrals wisely because there are no infinitesimals in practice. Rather, there are sufficiently small masses of electrons and small scanties of electrons. Thus the theoretical results produced via infinitesimals may be a little bit different from a reality consisting of discrete particles. And in economics you will meet a great trouble if you interpret the Average Fixed Cost- =Fixed Cost/Quantity- as infinity when no product is produced. The solution is to realise the quantity should be integers instead of reals, which have been adopted only for the  convenience to apply calculus.

Hence the exactness might be some pure imagination in mathematicians' mind, and the difference between "exactly the same" and "just a little bit different" can be too small to test. And when it can be tested,  they just deny the reality. For example, they blame the reality cannot give a perfect circle(a polygon with infinity sides).

And I doubt the importance you've stated, for before Georg Cantor the calculus had been on a "closing" basis for so many years and it had been applied so well.

Recently they wanna move one step further to make personal blogs registered under real names, two years after they did the same thing to campus forums. Guess what they say? Freedom is not absolute. Can they report what they do everyday in government to us, for the freedom is not absolute thing? "Management"- so we are doomed to be censored and controled and "cared" by the big father, huh?

It's been limited in my country for a long long time...

I like toast in milk

I mean, how many times is 1 as  nothing?