The Language of Mathematics 1

[CajunCenturion]

Multiplying by 10 increases by 1 order of magnitude, not 1 order of magnitude plus .000...1.

That is correct. There is no addition of .000...1. But remember that 0.9999... is repeating infinitely before the multiplication and it is repeating just the same after the multiplication. The multiplication by 10 has no effect on the repeating non-terminating decimal portion of the value.
Additional reading
wikipedia
Ask Dr. Math Also, see references at bottom of page

You can have infinites within infinities. You an infinty +1, etc. You can have infinity x 2, which is an infinite series followed by another infinite series.

Yes, you can have infinities within infitinities. They are know as degrees of infinity. However, infinity, infinity + 1, and infinity * 2, are the same infinity, or to be more precise, all these infinities are of the same degree, or those sets of numbers have the same cardinality. If a 1-to-1 mapping can be established between two infinities, then the two infinities have the same cardinality. The cardinalilty is know by the Hebrew Letter Aleph ([ℵ])

The smallest infinity is the set of integers, or counting numbers, and has cardinality of [ℵ]₀ (Aleph-Null). The set of integers, odd integers, even integers, integers + 1, and integers * 2 all have the same cardinality because a 1-to-1 mapping can be established with the integers. The values on either side of the mapping do not have to be, and usually aren't the same, but as long as the 1-to-1 mapping exists, the size of the infinity is the same.

There are just as many even integers as there as integers. The mapping is E_n = I_n * 2 or conversely I_n = E_n [÷] 2
[tt]
Integer Even Integer
1 2
2 4
3 6
4 8[/tt]
For every integer there is exactly one corresponding even integer, and vice versa; for every even integer, there is exactly one corresponding integer. The values of corresponding entries are not equal, in this mapping, the even value is twice that of the integer value, but both sets still have the same number of terms. There is no integer that does not have corresponding even integer, nor is there an even integer that does not have a corresponding integer. That means that a 1-to-1 mapping exists, therefore the numbers of integers is same as the number of even integers, or mathematically speaking, both sets have the same cardinality, which is [ℵ]₀. When dealing with the cardinality of infinities, it is not the values of the terms that matter, it is the number of terms that matter.

Now, can we establish a 1-to-1 mapping between the integers and the real numbers. Let's start with the integer 1 which maps to the real number 1. What is the next highest real number, i.e., the real number that will map to the integer 2? It is unknown. No matter what answer is submitted, there is a real number halfway between that value and 1. Therefore, you cannot map the real numbers to the integers and since the real numbers is clearly the larger set, the real numbers have a higher degree of infinity than the integers. The set of real numbers has a cardinality of [ℵ]₁ (Aleph-One).

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[tgreer]

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[sbudzynski]

Proven Mathematically that girls are evil

Girls = Time * Money

Time is Money Time = Money
therefore Girls = Money * Money

Money is the root of evil
therefore Sq root of Money = Evil
therefore Money * Money = Evil

And Finally
since Money * Money = Evil
and Money * Money = Girls
Girls = Evil

A friend of mine sat down and showed me that, i dont know if the math is whats funny or the fact he no life as to show me a formula for it!

Steve Budzynski

 

[sbudzynski]

wait a minute

money is the root of evil
therefore money = sq root of evil
therefore money squared = sq root of evil squared

therefore money * money = evil

i knew something didnt look right!


Steve Budzynski

 

[SilentAiche]

FWIW:

I can prove, beyond any shadow of a debt, that

[purple]Tim <> Money[/purple]

er, Bob



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[Stella740pl]

Is Tim your name then?
Then who is Bob?

 

[sbudzynski]

i was wondering the exact same thing!

Steve Budzynski
Metro Office Products Inc

http://www.metoffpro.com

 

[Stella740pl]

Well, I guess Bob would be his uncle...

 

[sbudzynski]

or sig. other?

Steve Budzynski
Metro Office Products Inc

http://www.metoffpro.com

 

[Stella740pl]

This I would have no way of knowing and don't want to speculate.

Steve, I was refering to the expression discussed in thread1256-864031.

 

[Stella740pl]

Sorry, I was actually referring and not refering.

 

[sbudzynski]

i was just playing, but thanks for referring me to help understand the connection of your joke

Steve Budzynski
Metro Office Products Inc

http://www.metoffpro.com

 

[Stella740pl]

SilentAiche,

Now I remember you talking of capitalization of TH in THanks, and the silent 'H' in your name. So I guess you are Tim H., aren't you?

 

[SilentAiche]

EyeBeeTim...

Don't recall the exact post, but some time ago I impulsively signed "Bob" (and later, "Robert", hehe) when (I suppose) I was a bit embarrassed by whatever the heck it was I said. So, no, I'm not really "Bob." I'm Tim.

The really dumb thing about the "Bob" episode is that I totally failed to recognize that TT is an ever-evolving community. Someone like Steve probably missed most of the "Bob" posts, so they make no sense to him. [red]BTW, Steve - Welcome to Tek - Tips!![/red]

Stella: THanks for recalling the "TH" post; I actually just got through reading a new post of yours on language, and realized how really awful I am at foreign language skills.

THanks,
Tim








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[BobRodes]

Yes, when someone says something embarrassing, I can see why they confuse themselves as me.

Bob

 

[Stella740pl]

Tim,

I actually just got through reading a new post of yours on language,
Which one is that? The one in "You people" thread?

and realized how really awful I am at foreign language skills.
You see, English is not a foreign language for me any more. It used to be when I studied it in school, 5th grade through graduation; then several semesters in college. Now, it's the language of the country where I live and work, so it's not foreign. (Russian is my first language, and Ukrainian is the language of the country where I was born and grew up, even though less used than Russian in the area I am from.)

 

[SilentAiche]

Yes, when someone says something embarrassing, I can see why they confuse themselves as me.

To all the "Bobs" out there, please don't take my foolishness seriously. I was just substituting another 3-letter name...

Stella: I really don't recall the exact language post at this point, which may be just as well. I guess my point is that I'm genuinely impressed by folks who can learn to converse in languages to which they were not native-born.

Tim (really!)

(unless you disagree, then it's, er, RobertFreeway or something...)


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[craigsboyd]

Since Stella was clearly referring, and you've decided you're Bob (at least part time), I can only infer that you were the one refering. I would quit that nasty habit, lest you wake up as Ned tomorrow morning.

SweetPotato Software Website
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[SilentAiche]

10-4, CB:

Are you suggesting a joint resolution??

Tim


BTW - if anyone's wondering, I don't touch that crap. Me cloudy daze are cirrusly natural.


tim

Tim

TIM

tIM

tiM



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[Stella740pl]

Tim,

I guess my point is that I'm genuinely impressed by folks who can learn to converse in languages to which they were not native-born.

It's not that hard, honest. I can give you a few tips on that. ;-)


Move somewhere.

Take a few months of intensive classes that include grammar.

Buy some good dictionaries.

Get a job where your bosses and clients don't speak English.

Among colleagues speaking the language natively, spot a knowledgeable one that might be happy to answer questions.

Get a TV with no English programming, if at all possible, or just put them all on parental control and forget the password.

Turn on close captioning in the language you are learning (after about 2 years, you will start noticing errors in the captions; and after 3 they will get so annoying, you will turn them off).

Subscribe to a magazine on a familiar topic; pick up some newspaper - free will do.

Do you remember any book originally written in that language that you've read translated into English? Now it's time to buy the original and get busy with it. If you don't remember any, find a classical book originally written in that language; check with someone first if it's easy enough for a learner (some of them would be hard even for a native speaker).

Continue until you know the language, and don't stop even then - or you will forget. (Well, after several years, you can turn on some English TV programs, and a few books here and there.)

You can say that you are good at understanding the language when you start to understand humor on TV and in books (wait till you start to get the second layer of humor and cultural references - and you will).

You know that you are good at conversations when you are able to respond well to an insulting remark and to get necessary information over the phone - not relying on visual clues of personal conversation or Internet.

Of course, depending on the personal abilities to learn languages (and on age when they started, too) people learn at different pace and to a different degree.

If you actually decide to follow my advise, I would be interested to know the outcome, so keep me in the loop. ;-)

 

[SilentAiche]

Stella,

Many thanks for your response. I think we have, perhaps unintentionally, combined two thoughts here. I may start a thread on #2.

You outlined a remarkable 12+ point way to learn a non-native language. I have absolutely no doubt that your ideas would work very, very well. The funny thing? You probably have no idea how reluctant someone like me would be to trying them. The reason: I don't want to leave.

I don't want this to devolve into a standard "home-body" verses "world-traveler" discussion.

My roots here in North Carolina are very, very deep. I can trace my NC ancestry to about 1759, and even then they came from Virginia (another colony). As those "roots" progressed, I can't complain too badly about what opportunities they provided for me. In other words, I have had no compelling reason to leave.

On the other hand, where would America be but for her immigrants, those who DID have a compelling reason to leave their native countries?

My question, I guess we'll call it Question #2, is: What compels someone to emigrate? I (thanks be to God) have never faced such a question. What say the members of this community?

THanks,
Tim



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