Infinite Fun in Religious Maths!

[drsatish]

Infinite Fun in Religious Maths!

(This thread has been started in response to PolyHedral's reply to my post
"Is Altruism Darwinistic?")

Hi Poly,
When did you turn 'Religious'?

What are the symbols you used? 0 and a compound symbol.. which I CAN'T GRASP! Is that you lying prostrated before the cross?

Is 0 the same as the 'Void" of Buddha?

What is Really Infinity?

Is it really required in Maths?
Can't PRECISE Maths EXIST...without something VAGUE, INDESCRIBABLE?

Is the USE of the Infinity Symbol, the same as the USE of IDOLS...in Religion?

What is Infinity PLUS?

Satish
PS: Well, this will be a learning lesson for me (hopefully) from the Maths Folks here! Please don't use BIG HIEROGLYPHIC Formulas ...they look sort of like an 'orgy' to me...with no idea of who is on top of who or who is doing what to whom!

 

[angellous_evangellous]

No Sanskrit yet.

You'll need to be promoted to Sanskrit poetry now.

 

[PolyHedral]

Hi Poly,
When did you turn 'Religious'?

I'm not, in any conventional meaning of "religious."

What are the symbols you used? 0 and a compound symbol.. which I CAN'T GRASP! Is that you lying prostrated before the cross?

0, and S, the successor operator. S0 is commonly written 1, SS0 is 2, and so on, so forth. All else follows.

What is Really Infinity?

Is it really required in Maths?

Infinity is, essentially, how far you get when you count forever. And it is hardly required, but it is immensely helpful for some problems.

Can't PRECISE Maths EXIST...without something VAGUE, INDESCRIBABLE?

Yes. Mathematics can and is defined absolutely precisely. There is no vagueness, anywhere.

What is Infinity PLUS?

Plus what? Infinity? Infinity. Adding any finite value to infinity yields infinity. Adding two infinite numbers simply yields the bigger infinity.

 

[Breathe]

Adding two infinite numbers simply yields the bigger infinity.

A bigger infinity?

 

[PolyHedral]

A bigger infinity?

You end up with "bigger" infinities because of something called set theory. A set in mathematics is just a list of numbers, for instance, {5,284,28,193,0}. However, occasionally, you want to know the size of this set. For finite sets, you can just count them. However, when you are counting, you're actually doing some maths: you're translating each thing in the set into another number. For instance, in our previous example, {5,284,28,193,0}:
5 becomes 1,
284 => 2,
28 => 3,
193 => 4,
0 => 5.
And thus we know that there are 5 items in the set {5,284,28,193,0}. What we have found is that, if we can translate, or map, some set onto some other set, (as {5,284,28,193,0} became {1,2,3,4,5} above) we know that the sets are the same size.

However, it becomes slightly more complicated with infinite sets of numbers. The "smallest" infinity is what are called the "natural" numbers, what you get when you count 0,1,2,3,4,5... forever.

You get "bigger" infinities when you have a set that you cannot translate onto the natural numbers. However, this is a little sticky. For instance, imagine the even numbers, which go from 0, 2, 4, 6, etc. You would think that, since you're only using every second number, this would not be the same size as the natural numbers, wouldn't you? Not quite: for each and every even number, we can divide that number by 2, and thus we end up with the natural numbers. (0 just becomes 0, 2 becomes 1, 4 becomes 2, 6 => 3...) So the even numbers are the same size as the natural numbers. If you find this counter-intuitive, good: you're sensible.

For a set that is larger than the natural numbers, imagine the decimals. (Which include 1, 1/10th, 1/100th, 1/1000th, etc, but also include 2, 2.1, 2.01, and so on.) Obviously, 1, 2 and 3 are all decimal numbers. But so is 1.5, 1.25 and 1.0625, and there is no way to translate all of these at once onto the natural numbers. Therefore, there must be more decimals than there are natural numbers. But since we already took the amount of natural numbers as "infinity", that means there must be a more than infinite amount of decimals. There's your bigger infinity.

 

[Breathe]

Oh... I see. I think.

I'm not too good at mathematics, but I understood what you are saying. Thank you for taking the time explain it to me.

 

[TJ73]

You end up with "bigger" infinities because of something called set theory. A set in mathematics is just a list of numbers, for instance, {5,284,28,193,0}. However, occasionally, you want to know the size of this set. For finite sets, you can just count them. However, when you are counting, you're actually doing some maths: you're translating each thing in the set into another number. For instance, in our previous example, {5,284,28,193,0}:
5 becomes 1,
284 => 2,
28 => 3,
193 => 4,
0 => 5.
And thus we know that there are 5 items in the set {5,284,28,193,0}. What we have found is that, if we can translate, or map, some set onto some other set, (as {5,284,28,193,0} became {1,2,3,4,5} above) we know that the sets are the same size.

However, it becomes slightly more complicated with infinite sets of numbers. The "smallest" infinity is what are called the "natural" numbers, what you get when you count 0,1,2,3,4,5... forever.

You get "bigger" infinities when you have a set that you cannot translate onto the natural numbers. However, this is a little sticky. For instance, imagine the even numbers, which go from 0, 2, 4, 6, etc. You would think that, since you're only using every second number, this would not be the same size as the natural numbers, wouldn't you? Not quite: for each and every even number, we can divide that number by 2, and thus we end up with the natural numbers. (0 just becomes 0, 2 becomes 1, 4 becomes 2, 6 => 3...) So the even numbers are the same size as the natural numbers. If you find this counter-intuitive, good: you're sensible.

For a set that is larger than the natural numbers, imagine the decimals. (Which include 1, 1/10th, 1/100th, 1/1000th, etc, but also include 2, 2.1, 2.01, and so on.) Obviously, 1, 2 and 3 are all decimal numbers. But so is 1.5, 1.25 and 1.0625, and there is no way to translate all of these at once onto the natural numbers. Therefore, there must be more decimals than there are natural numbers. But since we already took the amount of natural numbers as "infinity", that means there must be a more than infinite amount of decimals. There's your bigger infinity.

What makes you so good is your ability to make that make sense! Thanks so much!

 

[drsatish]

Hi Poly,

Thanks for the explanation. I will try to "visualize" what you said.
Keep up the good work. In future, I will ask about Calculus. Please don't get turned off by my replies in the FUN part. Anyway, I don't know WHAT to ask in Calculus. So I might as well ask WHAT is Calculus!

Now for the FUN part.

I'm not, in any conventional meaning of "religious."

If not 'conventional', could it be 'stealthy' or 'nuclear'?
Terms used by ANGRY people....the MILITARY! (especially blue faced ones!)
Conventional warfare, Gureilla warfare, Stealth Bombers of US & recently stealthy China,
and Nuclear.

..Oh! man! Nuclear is OLD STUFF..more than 60 years old....used by grandfather generations...should we DE-CLASSIFY it, make it PUBLIC DOMAIN for Easy Download and Use by the General Public?

Should we rename it to Conventional Nuclear Warfare....?

Please don't ask 'what' the connection is!
It is Death!
The Very TOPIC of MILITARY & RELIGION!)
& Birth of Life & Protection of Life
The Very TOPIC of MILITARY & RELIGION!

0, and S, the successor operator. S0 is commonly written 1, SS0 is 2, and so on, so forth. All else follows.

This is a PURE RELIGIOUS STATEMENT!
In the Beginning there was Nothing or Everything...depending on how you look at that symbol...
After IT, effused S....omething, S.....omething.....and so on, so forth. All else follows.
Now I am sure...you are using an UNCONVENTIONAL Approach/Terminology!
Are YOU sure..you have NOT YET ....you know what!

Infinity is, essentially, how far you get when you count forever. And it is hardly required, but it is immensely helpful for some problems.

For ever? That is a PURELY RELIGIOUS TERM!

Hardly required....but immensely helpful for some problems.

How can something that is 'hardly' required be 'immensely' helpful?
Is that not a Contradiction of Preciseness?

Is there a Maths that has been developed WITHOUT USING Infinity?

Is there ANY PUBLICATION on the Status of Maths,
with ALL INFINITY SYMBOLS REMOVED..
..from ALL EXISTING MATHEMATICAL Equations, so far conceived by man?
..and consequently,
...ALL Other Equations....Referencing Those Equations with the Infinity Symbol.

Yes. Mathematics can and is defined absolutely precisely. There is no vagueness, anywhere.

What is PRECISE about Zero?
How can you be PRECISE about NOTHING?

Plain common sense says that if you remove nothing from something, the same something remains.

Can you tell me what remains when nothing is removed from Maths?
I mean 0 is removed from Maths!
No Zeroes ANYWHERE! (I believe Romans did not have Zero..)
But I am talking about 2011 Maths.
..0 removed from 2011 Maths.

With the PRECISE Maths that is Left,
A. What Precisely can YOU DO?
B. What Precisely you CANNOT DO?

If you say, nobody has done a Precise study on that yet,
I would say ..there are no Mathematicians on Earth! (Precise, of course!)

Plus what? Infinity? Infinity. Adding any finite value to infinity yields infinity. Adding two infinite numbers simply yields the bigger infinity.

Adding two infinite numbers simply yields the bigger infinity.
(Odion beat me to it on this one.)

Coherence level low...Vagueness level High!
bigger infinity! How can be something MORE than Infinity?.
...are you in Religious Dilemma as to Which God of Which Religion is Greater?
..Vagueness level High!

How many decimal numbers can you put after 1?
1.1
1.11
1.111....................INFINITY....?
..Does this MEAN there are INFINITE NUMBERS ...BETWEEN 1 & 2 ?

Now you are becoming ULTRA RELIGIOUS!
...THERE is INFINITY WITHIN the SMALLEST ME.....the Small-Self
...THERE is INFINITY....at the Edge....Beyond.... the True-Self

All these are Religious-Mathematics-Sound Statements:
1. The All is IN Me.
2. I AM in All.
3. I AM ALL.
4. ...but the Illusion is that 1.11 thinks it is ALL....egoism, megapride, hitlerism etc...

Hope it is AS CLEAR TO YOU....as your statement
1,2,3,4.......the Series....has EXACTLY THE SAME LENGTH
as
2,4,6,8.......the Even Series...

Oh! Man! That iS ODD!

Yours precisely,
Satish

 

[Twilight Hue]

..Does this MEAN there are INFINITE NUMBERS ...BETWEEN 1 & 2 ? -drsatish-

Actually that may be conceptually true via infinite division. How small can you go? :yoda: