Math Is Fun Forum

Ricky, I do not have a physical evidence that all that approximation has a stop point. I do have some for particular formulas which in fact deals with a multiple of smallest divisions - the formula to calculate mass and electricity, for example

And what is more, I have logical evidence that the concept "arbitarily small" embeds "infinitesimal" as an essential part and hence is paradoxy and hence cannot exist even before any physical evidence is found.

Let's define a pair of quantities, either one is larger than the other at the same time. I do not need to list all possible two quantities to convince you that such pair cannot exist through pure logic. And do you buy it? Do you just say that because I cannot find all pairs of quantities to present them in front of you so that you believe there is some room for such a paradoxy pair to really exist?

There is priori knowledge beyond empirical knowledge, and this is LOGIC. You are free to make assumptions and make definitions, but your assumption and definition cannot be self-contradictory.

And the proof of potential infinitesimal containing real infinitesimal was the main topic of my essay, the gravity break down was just the appetizer. I regret not putting the argument of priori knowledge in it to present it more convincing.

And forgive me for not sharing the proof just for now. I can give a hint, my proof only use rationals, or fractions, without even a touch on Reals, and it doesn't have to, since Reals are found on the assumption of all fractions' existence.

Now it seems correct.

Just like the neo-liberalism and market-fundamentalism. We haven't come up with a substitute, so folks just bear with it and listen to our preach it is the truth we know so far even we know its assumptions are ungrounded.

. Just as Euclidean geometry is "wrong" in the context of the real world, so are Newtonian mechanics. Yet, both are still extremely useful

Well, it doesn't mean we use them without recognizing their faults, and without knowing how they coincidentally discribes things right in some cases, but will definately fail in other cases.

If the assumption is wrong, the theory is doomed to fail in some cases, even if it looks right, funcitions well in other cases. History acknowledges this fact and people's ignorance very often.

before 100 years,their parents said to them that in that time,there were any serb around.Serbia has expulsed albanians from their houses,because that regions is a riched long plain  because of it's river,and tool albanians prorietary and give them to serbs wich tehy placed in the albanians proprieties.This is an "ethnic  cleaning

Again, before 200 years, what happened in America? 50 years ago, what happened in Palestan? You see, there is no justice in land. You can think it is just for you to own the land, while the other think they can own it too. Sometimes the native win, while other time the immigrants win. There is no justice whatsoever in this zero-sum game, everybody says they are right. What's behind is the power rules.

In this sense, I don't believe the international law, which is just conciliation by big powers.

This is to compute the weighed average life of maturity by discount value for Annuity.

An Annuity gives you A amount of every year.

Discount "all" of them to now gets you A/(1+r)+A/(1+r)[sup]2[/sup]+...=A/r

And the weighed average life is (1A/(1+r)+2A/(1+r)[sup]2[/sup] +...)/(A/r) = (1+r)/r

Oh I got it. Just deduct the first term and get substraction.

Post 5 is correct. Both the formula and the justification.

started violence in albian people

well officially it could be that Serbs started violence, but it may just as the same as the claim that Indians attacked whites in America.

I just need to remind you some group of people are prone to start violence in cordiance under the same rligion basis. This can happen in a large scale, as we observe in Indonesia Massacre, or in a small scale, local bully basis.

And above all, history is written by men. The source may determine its view point. Wars often start with good reason, but often than not, a war is a war, good reason is just one point. Remember the invasion to Greece? To establish a totalitarian government in order to fight communism? Remember the long history of totalitarism in Spain long after the WWII is over? These were under "good reasons". And ironically, Ben Laden was trained by US Intelligence Agency in 1970's during Afgan war, terrorist's technique, how to bomb, was taught to them. and they started their drug business ever since their start. But Uncle Sam just torlarated them, under "good reasons".

Saudi Arabia is authoritarian, but is never considered a threat, while Iran is democratic (at least more deomocratic than the former) but considered evil. But I will never be suprised that some day media (CNN, CNBC, BBC) will cover a small incident in Iran in a large scale for 1 month and for some "good reason", Iran is invaded. And I will never buy it, small things are often excuses, a country wouldn't be that noble to help out on the risk of their own soldiers, they have done the calculation already but won't show it. They often seek their interest or power under a noble excuse.

I personally believe that mathematics is a description of a pure universe rather than our real one, and that our real one is an approximation to that other universe.  But to me, existence in the pure universe means that it does indeed exist.

I got what you mean, Ricky. Sigh....

This is pretty much exactly what an analyst means when he says "as n goes to infinity".
But not. I deny indefinate increase in most times or indefinite decrease in all times. I have a stop point while the above has not.

Hmm, physics can fail, but mathematics cannot. Mathematics is perfect, the only imperfection is the reality. Even when they do not meet, it is other that should change but mathematics. Good point!

I guess you can start a religion, Mathematicism, Ricky. Don't know if the ancient Greeks agree with you if their souls live to today.

it will be like
0 d/2 d
G 4G G

thus from 0 to d/2, G is increased to 4G
but from ∈ to d/2, ∈>0, we know  it is decreasing
Uh hah, how does this happen? Where is the darn turning point?

Moreover, I can prove G(0) is not smaller than any number. And I think you don't need me to do so, do you?

Thus it is fair to conclude G(0)>any positive number, which is infinity.
Well if you only think infinity is a symbol ∞,
you don't really what it means, Ricky. And of course you assume I cannot prove out a symbol ∞.
It has a meaning beyond its name.