Math Is Fun Forum

"will educational standards decrease? "

Well I really found the Maths part of Japan's College Entrance Examination tough when I was excellent in high school in China.

Part of Culture, part of Language.

The debacle is, China don't have excellent college Education as Americans and Europeans do.

I think in terms of Arithmetrics, here is the advantage:

1 Yi
2 Err
3 San
4 S~/s/
5 Woo
6 Lyou
7 Tsi 
8 Ba
9 Jyow

Chinese words for figures are much shorter and thus easier to master than those of the English language

"It's a model."
Base 2 is a Better model, based on the reasons I have stated.

Then try it with: f(t) = C*2^(kt) + D.
I have already done it
f(x)=100*2^(xlog[sub]2[/sub]1.6)
C=100, k=log[sub]2[/sub], D=0
Doesn't it fit in the data?

"Infinity + 1 = Infinity doesn't make sense, but neither does Infinity + 1 != Infinity, because you're treating infinity like a number when it isn't one.  Until you accept the nature of infinity, discussion of this topic is pointless."

Yes, you are switching infinity concept to a docile and flexible one. Well initially I assume you perceive it as stable and cannot change.

Well it is just simpler to disprove infinity in this sense.
Suppose you think the amount of elements in this
{2,3,4,5,...}
can vary.
(Infinity+k=Infinity)
And I wonder which element(s) can vary so that the whole amount of all the elements can vary?

Since if it has got infinity elements or infinity+1 elements doesn't matter at all. I wonder what is the +1 element that is totally disposable yet addible and doesn't make a difference at all?

BTW
When you have infinity+1=infinity
you assume
infinity[sub]1[/sub]+1=something
And this something qualifies as infinity too.
However, is it just the same as infinity[sub]1[/sub]?
No, it can be strictly qualified as non-finite and infinite,
But this doesn't guarantee you can treat them as equal.
Because infinity is not necessarily single and unique.
And we have just got two infinities here
One infinity[sub]1[/sub] and the other infinity[sub]1[/sub]+1
The latter strictly literally contains not only the former but also 1 more and is not equal to the former (in fact larger than).

And the fact that it is also non-finite doesn't lead to the conclusion that they are all the same.

It's just the same argument that we are both human, which doesn't prove we are all the same one.

You can relabel, OK? But you cannot simply state that your relabeled set is the same as a part of the original set. And you cannot then move on to use the same and new concept of large to disprove this concept because you haven't even reached the same condition yet.

Why have you made such a mistake in thinking them the same? Because you just see 2 in both, 3 in both, 4 in both, and elipse in both, and then you think that they are the same? I have pointed out this fallacy in Post 900.

And I have given the proof why they are not the same in Post 899. The relabeled
{2, 3, 4, ...}#
has one more member than the part
{2, 3, 4, ...}
in the original set
{1, 2, 3, 4, ...}
And this proof is based on your assumption that you have relabeled all the memebers of the original to the new {2, 3, 4, ...}#.
Since they have the same amount of member, a part of either one cannot have the same amount because the larger defination. (I will explain this in BTW)
And thus you cannot equate the relabeled to the part of the orginal because even they start at the same begining, they go on in seemingly the same pattern, they have different amount of elements after all!

Do you call
{2,3,4,5,...1001}
and
{2,3,4,5,...1000}
the same?

The same concept applies to this situation also. The only difference is that this is an infinite case. And in order to compare, I applied the larger concept.

BTW
The larger concept is quite equivalent to
the concept of
Part is smaller than the whole.
in philosophy.

(
The almost equivalence is as follows:
The whole has what all the part has, but also has something that it doesn't has, hence the whole is larger than the part. (or the part is smaller than the whole)
The back way:
A has all B has and has further something it doesn't. Select just the "all B has" in A and it is clearly a part in A because A has not only it but also something else. And this part equals B and hence is smaller than A. (Note this time the proof applies the equal concept, and that's why I said almost equivalence)
)

This concept is so far the most conservative defination in all the concepts of larger. I cannot find a more fundamental defination than this. If any other defination contradicts this one in some sense, we may examine that one is true or not.

"1 because you implicitly mapped d to d.  So both c and d map to d."

You forge this up, dude.

" my map is both 1-1 and onto.  "

Alright, let's stay with your mapping.
{2,3,4,5,...}#
How many have you mapped?
The same amount of
{1,2,3,4,...}?

And {2,3,4,5,...}# has lacked one symbol of 1 in it?
And yet it has the same amount.
And so it has one more symbol than the original subset {2,3,4,5,...} otherwise the mapping cannot be completed in the same amount.
And what is it? Isn't it the transformation of the last symbol in the old {1,2,3,4,...}?
And I can apply the same methodology to find the last symbol, just by comparing
{2,3,4,...} and a {2,3,4,...}# (which just have one more symbol than the former).

Unless you deny you have mapped all of the members in old {1,2,3,4,...} into the new {2,3,4,5,...}, which simply makes your "disproof" unvalid.

My defination stays on a real term basis instead of  a nominal term basis.
I clarify this now, don't cheat.

"Remember, numbers are just symbols"

Numbers are not just so. Don't belittle them as Cantor and the mathematicians after him does, plz.

They stands for meanings.

2 stands for solid 1 and 1.
If you have bought two sandwiches and the counter only gives you one, will you be outraged or not? Or will s/he say 1 and 2 are the same, just symbols?

one := 2
two := 3
three := 4
four := 5

When writting such a thing, you are defining
2 as the single unit,
and 3 as the single unit + the single unit.
Hence essentially your new 2 means the samething the old 1 does. It can take on a different symbol but its ESSENCE stays the SAME.

Back to your game
well the new
{2,3,4,5...} stands for the same thing the old
{1,2,3,4...} stands for,
it should be compared to the old {1,2,3,4..} by what old symbols it means or in both new symbols they mean and both are fair. Don't try to play a translation or a word puzzle by simply and wrongly mixing them up.

If I say a MIT is smaller than Massachussets  Institute of Technology, do you agree?
Well because the letters of the former is less than the latter.

But essentially they stands for the same thing!

You can use 1 2 3 4 or 2 3 4 5 or whatever. But you should know the meanings behind the letters, that 2=1+1=single+single or 3=2+2=single+single. Don't try to blend them together or you are just fooling around saying something like one dime is smaller than five cents because one is smaller than five.

Perhaps you are just asking for trouble. Before constructing these sets, My logical argument has already stopped having an infnite set of all integers. And irrationals with infinite decimals may not exist at all.

And after all, we live in a common sense world, not in a maths fairy tale world. Many mathematical problems are just a waste of time since they are created so different than the real world and thus never get a chance to apply to it. (Infinity and surreals for example)

The same thing for equal and larger in my earlier argument
Amount of elements of {1, 2, 3, 4, ...} = Amount of elements of {2, 3, 4, 5,...}
Because every member of the latter gets 1 added from the former.
(You can say I cannot do this, but please tell from where, since I know any number in the former set can be added by 1)

And {1,2,3,4,5,...}# is larger than {2,3,4,5,...} because  it is generate by duplicating the latter and adding in a new element, an element does not belong to the latter. Thus it is larger according to my defination in common sense. What's your problem with this?

And the last part, transivity. Do you want to say that it is not transible for infnity?
Infinity+1=Infinity?
Then what's your infinity exactly? It's not stable? It's docile? It can be added in something and stays the same? Riduculous as it is, I have a refutation for this already in the previous post.