Wow, your teachers suck. -_-
How about pi?I think it is.
Or (22 / 7) (isn't that supposed to be pi?)
How about pi?I think it is.
Or (22 / 7) (isn't that supposed to be pi?)
Pi = the world's gayest number.
How about pi?I think it is.
Or (22 / 7) (isn't that supposed to be pi?)
Pi = the world's gayest number.
No, it's not. It's moderately close, but using a Pi constant on calculators is a lot more accurate than using 22/7.
Anyone here work at TI and know how that's done? I figure its probably 4*ATan(1) rounded to the nearest millionth or something.
If infinity isn't a number, is e? I recently had a conversation with my math teacher about "the number e" (Euler's number)
If infinity isn't a number, is e? I recently had a conversation with my math teacher about "the number e" (Euler's number)
e isn't infinite. It comes really close, seeing as how it's a constant.
How about pi?
Or (22 / 7) (isn't that supposed to be pi?)
The question is, do you consider "e" to be a number? I believe it is, just an irrational one.
Of course it is. We say the word number when we refer to "real numbers." And irrational numbers are a subset of real numbers.
If infinity isn't a number, is e? I recently had a conversation with my math teacher about "the number e" (Euler's number)
(http://images.google.com/imgres?imgurl=http://thesaurus.maths.org/mmkb/media/png/Infinity.png&imgrefurl=http://thesaurus.maths.org/mmkb/entry.html%3Faction-entryByConcept%26id%3D961%26langcode%3Den%26expand%3D0&h=160&w=300&sz=15&tbnid=EKJPI77eCbAJ:&tbnh=59&tbnw=111&hl=en&start=1&prev=/images%3Fq%3Dinfinity%26svnum%3D10%26hl%3Den%26lr%3D%26safe%3Doff%26client%3Dfirefox%26rls%3Dorg.mozilla:en-US:unofficial%26sa%3DN) rounded to the nearest tenth is (http://images.google.com/imgres?imgurl=http://thesaurus.maths.org/mmkb/media/png/Infinity.png&imgrefurl=http://thesaurus.maths.org/mmkb/entry.html%3Faction-entryByConcept%26id%3D961%26langcode%3Den%26expand%3D0&h=160&w=300&sz=15&tbnid=EKJPI77eCbAJ:&tbnh=59&tbnw=111&hl=en&start=1&prev=/images%3Fq%3Dinfinity%26svnum%3D10%26hl%3Den%26lr%3D%26safe%3Doff%26client%3Dfirefox%26rls%3Dorg.mozilla:en-US:unofficial%26sa%3DN)
Joe > Sidoh.
EDIT -
Nice, google </3 hotlinkers.
If infinity isn't a number, is e? I recently had a conversation with my math teacher about "the number e" (Euler's number)
In case there's some question about whether i is a number:
- We know that x + 1 = 0 is a valid equation; however, if we only had regular "counting" numbers available, we couldn't solve it. We would have to invent a concept of negative numbers, which we are all comfortable with .
- Then we have the equation x2 + 1 = 0. It also had no solution without inventing the concept of imaginary numbers.
--> Imaginary numbers are negative numbers are both pretty abstract. We can't see or touch either, but they seem to be numbers in a purely mathematical sense.
Ok, so the next question is, is 0 a number? It seems that 0 is just a placeholder. Doesn't "0" represent the lack of a number, not an actual number?
If 0 is a number, is it even or odd? What is the definition of even and odd that shows that 0 is even? Can it be shown that 0 also fits into the odd category?
Is the 0 in 2304 the same as the number 0? How are they related?
What is x in 2x = 6? Is it a number? It doesn't look like a number, but to anybody with more than a few years of math experience, it's immediately obvious that it's 3. If x can be considered a number, is it possible that our definition of numbers isn't as clear as we think?
What about x in 0x = 6? Is x still a number? Any number, real, rational, irrational, imaginary, etc. can be place in front of the x. But when the number 0 is, x no longer has a value. It seems like 0 isn't behaving as a number here.
Or, is there a case for considering 1/0 to be a number? Is the result infinite or undefined? Why? Is there a case for looking at it either way?
I think this is the most important question of all:
How are 0 and infinite related? Think about how to get the result of infinite in a finite equation. The only way to get it is to use a 0. This means that 0 and infinite are related, and that infinite can be derived from 0. Because, as it was already discussed here, infinite isn't a number, does that show that 0 isn't either?
By the way, most of these questions were inspired by or ripped from a variety of sources. I post them here to provoke discussion, and maybe we'll all learn something. :)
In case there's some question about whether i is a number:
- We know that x + 1 = 0 is a valid equation; however, if we only had regular "counting" numbers available, we couldn't solve it. We would have to invent a concept of negative numbers, which we are all comfortable with .
- Then we have the equation x2 + 1 = 0. It also had no solution without inventing the concept of imaginary numbers.
--> Imaginary numbers are negative numbers are both pretty abstract. We can't see or touch either, but they seem to be numbers in a purely mathematical sense.
Ok, so the next question is, is 0 a number? It seems that 0 is just a placeholder. Doesn't "0" represent the lack of a number, not an actual number?
If 0 is a number, is it even or odd? What is the definition of even and odd that shows that 0 is even? Can it be shown that 0 also fits into the odd category?
Is the 0 in 2304 the same as the number 0? How are they related?
What is x in 2x = 6? Is it a number? It doesn't look like a number, but to anybody with more than a few years of math experience, it's immediately obvious that it's 3. If x can be considered a number, is it possible that our definition of numbers isn't as clear as we think?
What about x in 0x = 6? Is x still a number? Any number, real, rational, irrational, imaginary, etc. can be place in front of the x. But when the number 0 is, x no longer has a value. It seems like 0 isn't behaving as a number here.
Or, is there a case for considering 1/0 to be a number? Is the result infinite or undefined? Why? Is there a case for looking at it either way?
Division: 0 / x = 0, for nonzero x. But x / 0 is undefined, because 0 has no multiplicative inverse, a consequence of the previous rule. For positive x, as y in x / y approaches zero from positive values, its quotient increases toward positive infinity, but as y approaches zero from negative values, the quotient increases toward negative infinity. The different quotients confirms that division by zero is undefined.
I think this is the most important question of all:
How are 0 and infinite related? Think about how to get the result of infinite in a finite equation. The only way to get it is to use a 0. This means that 0 and infinite are related, and that infinite can be derived from 0. Because, as it was already discussed here, infinite isn't a number, does that show that 0 isn't either?
Also, pi is not only a number, but the 16th letter in the greek alphabet.It's also a function. Also, it's another (different) function. So, pi is officially a letter, number, and two functions. Hrm.
(http://yoni.valhallalegends.com/greek/small-16.gif)
Sweet, I sparked a nice conversation by being an idiot!
rabbit: What do you mean Pi itself is a function?
Rational Numbers- Can be written as a result of the calculation: a/b. This includes repeating decimals, such as 5/7 or 1/3.I may be wrong. But, don't raitonal numbers have numbers that repeat after teh decimal? Such as .3333333 ect. But, 5/7 doesn't fit the description, so did you mean to put that in irrational? Or am I just wrong?
You're just wrong :-PQuoteRational Numbers- Can be written as a result of the calculation: a/b. This includes repeating decimals, such as 5/7 or 1/3.I may be wrong. But, don't raitonal numbers have numbers that repeat after teh decimal? Such as .3333333 ect. But, 5/7 doesn't fit the description, so did you mean to put that in irrational? Or am I just wrong?
@iago, Actually, I believe irrational numbers do not contain rational numbers, as irrational numbers cannot be written as "a/b".You are correct, Real numbers are the set of rational numbers plus irrationational numbers, like the set of all numbers contains real and imaginary numbers, whcih are mutually exclusive. ;)
Ah, you're right, I was mixing up irrational and real. Stupid mistake :)@iago, Actually, I believe irrational numbers do not contain rational numbers, as irrational numbers cannot be written as "a/b".You are correct, Real numbers are the set of rational numbers plus irrationational numbers, like the set of all numbers contains real and imaginary numbers, whcih are mutually exclusive. ;)
The first pi function (lowercase pi, as we usually see it), is the number of primes less than the argument.That seems off. Number of primes less than 60 is not 46.7 billion. They are: 2,3,5,7,11,13,17,19,23,27,31,37,41,43,47,53,57.
IE:
(http://img318.imageshack.us/img318/3135/pi13yd.png)
The second pi function (uppercase pi) is the expression for the process of Eratosthenes' Sieve (the multiplication of all factors of the argument).
IE:
(http://img318.imageshack.us/img318/9586/pi23rd.png)
The only possible way I could think to produce ∞ from an equation would be x*0=0. But as that is undefined, I do not see any other way.x*0 equals 0. It's defined as 0, isn't it? anything * 0 is 0, or so I thought.
e is like pi, I believe. My ti-83 says it's approximately 2.71828182. If by "like infinity" you mean not a number, then no, it's a number. It's more like Pi in that they are both irrational numbers. I would, however, relate it more closely to phi (phi is approximately 1.618...), because both were discovered frequently in nature. Phi is a very interresting number.
-EDIT-QuoteThe only possible way I could think to produce ∞ from an equation would be x*0=0. But as that is undefined, I do not see any other way.x*0 equals 0. It's defined as 0, isn't it? anything * 0 is 0, or so I thought.
Wrong :-*! 0! = 1.
Wrong :-*! 0! = 1.Oh yeah that's right. *reaches back 3 years* I remember arguing over that with my calculus teacher. He won.
Oh yeah that's right. *reaches back 3 years* I remember arguing over that with my calculus teacher. He won.
Basically, its that you can only arrange nothing in one way.
By the way, here's another math problem: Are there more natural numbers (1, 2, 3, ...) or integers (...., -2, -1, 0, 1, 2, ....)?Well, there's an infinate number for both, one just gets to infinity slightly faster :)
For every natural number x, there are two integers, x and -x. So there are twice as many integers as naturals numbers, plus 1 (for 0). Right?
There are varying levels of infinity. Numerically, as in counting from 1, 2 ,3, 4 etc, they are infinity, but cardinally, as in {1, 2, 3, ...}, integers are greater. I believe they are alaph numbers..Rational, whole, natural, etc., are all "countable" infinite sets. So is Real, apparently, but we haven't proven that one yet.
[Edit]: Whoops, Aleph* Numbers (http://en.wikipedia.org/wiki/Aleph_number)
Not reach infinite, be infinite. :o
Actually, if either could reach infinity, neither would be faster.
We're not talking about whether either could reach infinity, we're talking about the value of the count of numbers in the series. Integers have 2 x (count of whole numbers) + 1 items. Assuming (count of whole numbers) is infinity, the count of integers is 2x(whole numbers count infinity) + 1, which makes it a bigger infinity.
If you put (whole numbers count infinity) / (count of integers infinty) you'd get a value infinitesimally approaching 0.5 from the left.
N| 1 2 3 4 5 6 7 ....
------------------------
Z| 0 1 -1 2 -2 3 -3 ....
e is like pi, I believe. My ti-83 says it's approximately 2.71828182. If by "like infinity" you mean not a number, then no, it's a number. It's more like Pi in that they are both irrational numbers. I would, however, relate it more closely to phi (phi is approximately 1.618...), because both were discovered frequently in nature. Phi is a very interresting number.
-EDIT-QuoteThe only possible way I could think to produce ∞ from an equation would be x*0=0. But as that is undefined, I do not see any other way.x*0 equals 0. It's defined as 0, isn't it? anything * 0 is 0, or so I thought.
I think those things have already been mentioned. :P
x * 0 = 0 is one way to think of infinitie, but since you can't devide by zero due to mathematical laws, it's undefined, not infinite.
Technically, dividing something means splitting it into equal piles. A good way of thinking of this is dealing cards. How do you deal cards to 0 people?
52/0 = 0R52 (you didn't give anyone any cards) = 1.
Division by 0 equals 1.
By your example, you'd be giving out cards forever, because you'd be sitting there with the deck giving one to each of the 0 people. So your deck would never lose a card. So it would work out to infinity, or undefined, depending on how long you sit around, I suppose..e is like pi, I believe. My ti-83 says it's approximately 2.71828182. If by "like infinity" you mean not a number, then no, it's a number. It's more like Pi in that they are both irrational numbers. I would, however, relate it more closely to phi (phi is approximately 1.618...), because both were discovered frequently in nature. Phi is a very interresting number.
-EDIT-QuoteThe only possible way I could think to produce ∞ from an equation would be x*0=0. But as that is undefined, I do not see any other way.x*0 equals 0. It's defined as 0, isn't it? anything * 0 is 0, or so I thought.
I think those things have already been mentioned. :P
x * 0 = 0 is one way to think of infinitie, but since you can't devide by zero due to mathematical laws, it's undefined, not infinite.
Technically, dividing something means splitting it into equal piles. A good way of thinking of this is dealing cards. How do you deal cards to 0 people?
52/0 = 0R52 (you didn't give anyone any cards) = 1.
Division by 0 equals 1.
By your example, you'd be giving out cards forever, because you'd be sitting there with the deck giving one to each of the 0 people. So your deck would never lose a card. So it would work out to infinity, or undefined, depending on how long you sit around, I suppose..
Division is more accurately described as "division among/between". IE: Division by 1 means "division among 1", and thus the source remains whole, as it all goes to 1 "thing".e is like pi, I believe. My ti-83 says it's approximately 2.71828182. If by "like infinity" you mean not a number, then no, it's a number. It's more like Pi in that they are both irrational numbers. I would, however, relate it more closely to phi (phi is approximately 1.618...), because both were discovered frequently in nature. Phi is a very interresting number.
-EDIT-QuoteThe only possible way I could think to produce ∞ from an equation would be x*0=0. But as that is undefined, I do not see any other way.x*0 equals 0. It's defined as 0, isn't it? anything * 0 is 0, or so I thought.
I think those things have already been mentioned. :P
x * 0 = 0 is one way to think of infinitie, but since you can't devide by zero due to mathematical laws, it's undefined, not infinite.
Technically, dividing something means splitting it into equal piles. A good way of thinking of this is dealing cards. How do you deal cards to 0 people?
52/0 = 0R52 (you didn't give anyone any cards) = 1.
Division by 0 equals 1.