"This would be easy to read by anyone who can read a clock." Yeah true. But then thats when we start moving poo. I.e. making Pi to be 3 hours, 14 minutes, 15 seconds, etc. rather than 3pm.

Math was never my best subject. Actually to be honest it was my worst subject. I was in special classes for math from like 4th grade all the way to senior year. I still like this clock though.

I took 21 hours of math, and I haven`t a clue on 3. 11 is just A hexadecimal number. 0x is the prefix that says what follows is a hexadecimal number, and 0B is 11 (08, 09, 0A, 0B, 0C, 0D, 0E, 0F, 10, 11...)

Here: 1. Legendre`s Constant 2. ??? 3. Unicode HTML 4. Modular arithmetic 5. Golden Mean 6. Factorial 3 7. 6.99999... 8. Binary (1x2^3 + 0x2^2 + 0x2^1 + 0x2^0) 9. Base-4 (like Binary is Base 2 and Hex is Base 16, this is Base 4 numbering) 10. Binomial Coefficient 11. Hexadecimal 12. Cube root=inverse of 12^3

Found it thanks to Google, number 2 is a reference to a joke about infinite parabolic curves which become closer to the integer with each iteration without every equalling it.

The joke is: An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The fourth, one-eighth of a beer. The fifth, one-sixteenth of a beer. The sixth...

The bartender says "You`re all idiots", and pours two beers.

@lionhart2, I hate that joke. It bothers me so much because the bartender is the idiot. Just like "7" on this clock, 6 repetend 9 does not equal 7. EVER.

You can`t call trashcan an idiot because his way of thinking is supported by many (if not most) mathematicians. I just choose to look at it differently.

seriously, all you people who think 0.999 repeating is NOT 1 need to go to class and listen -_-

There are various ways to prove it, but here`s a simpler way too look at it. 1/9 is 0.1repeating. x/9 is 0.xrepeating. So what is 9/9? 0.9repeating which equals 1.

I believe that what trashcan7 is trying to say is that the number .999999 repeating to infinity becomes a number so very close to the integer 1 that it actually can be evaluated as the number 1, with little deviation. It`s called the limit of a number

Yes, jazz. But many people, including me, view it differently. They could have used a non-controversial way of representing 7 (that would have appeased everyone).

Asymptotes. A number can get as close to x without ever reaching it. theorectically, you can keep putting 9`s after the decimal and it should never tough the asymptote. Of course this is just my way of thinking.

0.999_ = 0.9+0.09+0.009+... a=0.9 r=1/10 With infinite terms: 0.9/(1-1/10)=0.9/0.9 = 1 So 6.999_ does equal 7 Still, believe what you want and call others idiots for disagreeing. Commence insults.

> Stelly and Others > 6 repetend 9 does not equal 7. EVER.

Correct - I agree that for a "math geek clock" that is MATHEMETICALLY correct. However, since other number systems are present here, such as the human system called "time", if it was .0000000000001 seconds before 7 o`clock and someone asked you the time, you`d round it and say "7 o clock". Obviously, we`d all be a lot happier if they had used `approximately equal to` on the clock, but you`re right, a recurring decimal never actually equals the integer.

@lionhart2, I hate that joke. It bothers me so much because the bartender is the idiot. Just like "7" on this clock, 6 repetend 9 does not equal 7. EVER.

I read the joke as a contrast between everyday practicality and abstract maths.

The bartender`s action addresses the issue in a fast and effective way - the second pint will be enough to meet the orders of the mathematicians because between them they will never quite drink the whole pint.

you`re right, a recurring decimal never actually equals the integer. No, you`re wrong. 6.999... = 7.

6 repetend 9 does not equal 7. EVER. You just had to include that hearty "EVER" at the end didn`t you? I suppose if you didn`t there might just be times when it does equal 7, as if the terms somehow felt the need to be equal.

Actually, look closely enough and you`ll see that 11/9 IS a bunch of 11 repeatings. Only each one occupies 2 decimal places. 1.1, 0.11, 0.011, 0.0011... Add them all up and you get 1.22repeating. But anyway, you`re missing the point. This is just a simplified explanation. If you`re interested in the more lengthy ones, you could probably just look up the proof on the internet. I know its in my notes somewhere here but i`m much too lazy to look for it now haha.

1. Legendre`s constant (historical since B = 1). I would`ve used something more fun for 1 like -e^{i Pi}, but oh well

2. Imagine the result of that sum is "S", so: S = 1 + 1/2 + 1/4 + ... 2S = 2 + 1 + 1/2 + 1/4 + ... Now, 2S - S = S = 2 It`s not approximate, since the sum is infinite, this is an exact result.

3. Unicode HTML in hex for numbers, except I have no idea where the i comes from, 3 can be easily represented as 3

4. Using the definition of inverse modulo, bb^{-1} = 1 mod 7 1 mod 7 = 1, It`s the numerator in 1/7. So let`s find the number that has the same numerator when divided by seven and multiplied by (2^{-1})^{-1} = 2 8/7 = 1 + 1/7, so bb^{-1} = 8, and since b^{-1} = 2, that makes b = 4. In this notation, b^{-1} is NOT 1/b.

5. The golden ratio is (1 + sqrt(5))/2 = f, so 2f - 1 = sqrt(5) and its square is 5

7. (The controversial one), if 6.999... wasn`t infinite, then you`d be right, it wouldn`t be 7. But in a space that admits infinities, you can`t make a distinction between 6.999... < 7 < 7.0000... because there`s no concept of sequence for infinities, same as with 2., this is also an exact result. (See Galileo`s paradox to see why you can`t make sequences with infinities, if you count every number in an infinite sequence, and you count the number of squares in the same sequence you find that they both have the same number of elements, which is wrong because every square is in the same sequence. 1,2,3, ... inf, is gonna have inf numbers. but 1, 4, 9, ... is also going to have inf numbers, but the second sequence "should" be smaller since every number of it is contained in the first one.)

8. Binary, from right to left: 0*(2^0) + 0*(2^1) + 0*(2^2) + 1*(2^3) = 8

9. Base 4: 1*(4^0) + 2*(4^2) = 9 (why so many bases? so far it`s been 2 hex,

9. Base 4: 1*(4^0) + 2*(4^2) = 9 (why so many bases? so far it`s been 2 hex, one binary and one 4 ...) Also, I always write them backwards because I like 0,1,2,...,n instead of n,...,3,2,1,0

10. (5 2) = 5!/(3!2!) = 120/(6*2) = 10

11. Base 16, where A = 10, B=11, ... and the UNIX prefix 0x is used: 0x0B = 0B(Hex) = 11*(16^0) + 0*(16^1) = 11

12. 12*12*12 = 1728, so it`s cubic root is 12. It would`ve been more fun to write 1729 + i^2, if only because 1729 is a much more interesting and convoluted number.

For those of you still caught in the days of the ancient Greeks and do not believe in the convergence of a repeating number or series I submit to you two proofs: 10(.99...)=10/9=9.99... (10-1)(.99...)=9/9=9.99...-.99...=9 9(.99...)=9 therefore .99...=1 Or if you do not believe that we can use physical evidence with Xeno`s paradox with an infinite series which approaches 1 slower then .9 repeating (ie if it converges so must .99...; before one travels 1 foot they must first travel .5 feet then .25 feet and so on; if this never adds to one then then all movement is impossible. The B is legrende`s constant which is based on a series using the prime counting function, 11 and 9 are just different bases and 10 is not a matrix function but 5 choose 2.

@tozhan I don`t really think that proof is valid. You need to show why 10X-X=9. The person who doesn`t understand that .999... = 1 won`t really understand that the decimal portion of 10X equals the decimal portion of X.

yanging... even those who disagree that .999...=1 would disagree with your statement.

Do you know what .99... means? It means that the 9 is repeating infinitely. You can`t say .99... *10= 9.90; that`s completely ignoring what the proof is telling you.

Anyways, I can`t believe you don`t believe that .99... is not 1. You can`t look at it differently; that`s the beauty of math: it`s straight-up true or not.

"Here: 1. Legendre`s Constant 2. ??? 3. Unicode HTML 4. Modular arithmetic 5. Golden Mean 6. Factorial 3 7. 6.99999... 8. Binary (1x2^3 + 0x2^2 + 0x2^1 + 0x2^0) 9. Base-4 (like Binary is Base 2 and Hex is Base 16, this is Base 4 numbering) 10. Binomial Coefficient 11. Hexadecimal 12. Cube root=inverse of 12^3

If you`re still wondering what they are, look up in the more comments: page 1 should still have my posts where they`re all explained in detail (it`s 3 posts).

Technically, this clock isn`t only for geeks. Yes, they are the ones who`d get a kick out of it, but you would have to be a complete idiot not to know which numbers the equations translate to.

Frig me gently, I had no idea we had so many resident math nerds here at IAB. And many unfamiliar users who stay quiet through the standard-fare religious, political and ideological flame wars, but who come out gunning at the first hint of a bit of math.

Don`t get me wrong, I`m not poking fun, I love this.

IAB is a complex community, with many undercurrents and subcultures...

- For everyone else, just expect to be late to everything...
Thanks for clearing that up... )-|

Yeah true. But then thats when we start moving poo.

I.e. making Pi to be 3 hours, 14 minutes, 15 seconds, etc. rather than 3pm.

8`s not so wicked either.

But I approve.

I know what the means ;-;

Looked at comments. Everyone got 3 factorial.

v.v

*Why is that three so excited?*

sarcasm offline

This clock just tells me I need to learn more mathematics.

Math fail!

I took 21 hours of math, and I haven`t a clue on 3. 11 is just A hexadecimal number. 0x is the prefix that says what follows is a hexadecimal number, and 0B is 11 (08, 09, 0A, 0B, 0C, 0D, 0E, 0F, 10, 11...)

11 is being being expressed in hexadecimal, so that`s just a change of base.

I don`t even recognise the symbols used in 3.

> Can someone explain 3 and 11?

Here:

1. Legendre`s Constant

2. ???

3. Unicode HTML

4. Modular arithmetic

5. Golden Mean

6. Factorial 3

7. 6.99999...

8. Binary (1x2^3 + 0x2^2 + 0x2^1 + 0x2^0)

9. Base-4 (like Binary is Base 2 and Hex is Base 16, this is Base 4 numbering)

10. Binomial Coefficient

11. Hexadecimal

12. Cube root=inverse of 12^3

No idea on number 2.

The joke is:

An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The fourth, one-eighth of a beer. The fifth, one-sixteenth of a beer. The sixth...

The bartender says "You`re all idiots", and pours two beers.

3 is formatted for an ASCII 3 in hex,

11 is "B" in hex.

Lionhart: 2 is the infinite sum 1+1/2 + 1/4 + 1/8... = 2

for science or math "geeks", they`re not very bright.

No it doesn`t. It means that you are infinitely coming closer to 2 by an infinitely smaller number.

You can`t call trashcan an idiot because his way of thinking is supported by many (if not most) mathematicians. I just choose to look at it differently.

There are various ways to prove it, but here`s a simpler way too look at it. 1/9 is 0.1repeating. x/9 is 0.xrepeating. So what is 9/9? 0.9repeating which equals 1.

So x=11 11/9 Does not equal 0.11repeating.

LOOK IT UP.

6.999_ = 6 + 0.999_

0.999_ = 0.9+0.09+0.009+...

a=0.9 r=1/10

With infinite terms:

0.9/(1-1/10)=0.9/0.9 = 1

So 6.999_ does equal 7

Still, believe what you want and call others idiots for disagreeing. Commence insults.

> 6 repetend 9 does not equal 7. EVER.

Correct - I agree that for a "math geek clock" that is MATHEMETICALLY correct. However, since other number systems are present here, such as the human system called "time", if it was .0000000000001 seconds before 7 o`clock and someone asked you the time, you`d round it and say "7 o clock". Obviously, we`d all be a lot happier if they had used `approximately equal to` on the clock, but you`re right, a recurring decimal never actually equals the integer.

I read the joke as a contrast between everyday practicality and abstract maths.

The bartender`s action addresses the issue in a fast and effective way - the second pint will be enough to meet the orders of the mathematicians because between them they will never quite drink the whole pint.

No, you`re wrong. 6.999... = 7.

6 repetend 9 does not equal 7. EVER.

You just had to include that hearty "EVER" at the end didn`t you? I suppose if you didn`t there might just be times when it does equal 7, as if the terms somehow felt the need to be equal.

"I only understand 3".

Do you mean 3! which is 6, or do you mean the actual 3?

Here is an example: 1/3 = .3333...

so 3/3 = .9999...but also 1

It`s the same.

3! means you multiply that number by the numbers before it going down to 1. Example:

3x2x1 = 6

http://en.wikipedia.org/wiki/Factorial

1, 2, 3, 4...

> i can tell you what every number it means is: 1, 2, 3, 4...

DAMN but you`re good at that math thingy!

If I hadn`t already given the Comment of the Day Award for today, you`d have just go it I think

Actually, look closely enough and you`ll see that 11/9 IS a bunch of 11 repeatings. Only each one occupies 2 decimal places. 1.1, 0.11, 0.011, 0.0011... Add them all up and you get 1.22repeating. But anyway, you`re missing the point. This is just a simplified explanation. If you`re interested in the more lengthy ones, you could probably just look up the proof on the internet. I know its in my notes somewhere here but i`m much too lazy to look for it now haha.

Or the 6.. That one`s easy too, and I ain`t finished Highschool yet! ...Or our equivalent, that is.

1. Legendre`s constant (historical since B = 1). I would`ve used something more fun for 1 like -e^{i Pi}, but oh well

2. Imagine the result of that sum is "S", so:

S = 1 + 1/2 + 1/4 + ...

2S = 2 + 1 + 1/2 + 1/4 + ...

Now, 2S - S = S = 2

It`s not approximate, since the sum is infinite, this is an exact result.

3. Unicode HTML in hex for numbers, except I have no idea where the i comes from, 3 can be easily represented as 3

4. Using the definition of inverse modulo, bb^{-1} = 1 mod 7

1 mod 7 = 1,

It`s the numerator in 1/7.

So let`s find the number that has the same numerator when divided by seven and multiplied by (2^{-1})^{-1} = 2

8/7 = 1 + 1/7, so bb^{-1} = 8, and since b^{-1} = 2, that makes b = 4. In this notation, b^{-1} is NOT 1/b.

5. The golden ratio is (1 + sqrt(5))/2 = f, so 2f - 1 = sqrt(5) and its square is 5

6. 3! = 1*2*3 = 6

6.999... < 7 < 7.0000...

because there`s no concept of sequence for infinities, same as with 2., this is also an exact result.

(See Galileo`s paradox to see why you can`t make sequences with infinities, if you count every number in an infinite sequence, and you count the number of squares in the same sequence you find that they both have the same number of elements, which is wrong because every square is in the same sequence. 1,2,3, ... inf, is gonna have inf numbers. but 1, 4, 9, ... is also going to have inf numbers, but the second sequence "should" be smaller since every number of it is contained in the first one.)

8. Binary, from right to left: 0*(2^0) + 0*(2^1) + 0*(2^2) + 1*(2^3) = 8

9. Base 4: 1*(4^0) + 2*(4^2) = 9

(why so many bases? so far it`s been 2 hex,

(why so many bases? so far it`s been 2 hex, one binary and one 4 ...) Also, I always write them backwards because I like 0,1,2,...,n instead of n,...,3,2,1,0

10. (5 2) = 5!/(3!2!) = 120/(6*2) = 10

11. Base 16, where A = 10, B=11, ... and the UNIX prefix 0x is used:

0x0B = 0B(Hex) = 11*(16^0) + 0*(16^1) = 11

12. 12*12*12 = 1728, so it`s cubic root is 12.

It would`ve been more fun to write 1729 + i^2, if only because 1729 is a much more interesting and convoluted number.

10(.99...)=10/9=9.99...

(10-1)(.99...)=9/9=9.99...-.99...=9

9(.99...)=9

therefore .99...=1

Or if you do not believe that we can use physical evidence with Xeno`s paradox with an infinite series which approaches 1 slower then .9 repeating (ie if it converges so must .99...; before one travels 1 foot they must first travel .5 feet then .25 feet and so on; if this never adds to one then then all movement is impossible. The B is legrende`s constant which is based on a series using the prime counting function, 11 and 9 are just different bases and 10 is not a matrix function but 5 choose 2.

.999999....=3/3=1/3+1/3+1/3=1

I scroll down to the comments and everyone`s doing maths.

Why do the maths when you know the answer? (and don`t know how to do the maths)

X=0.99...

10X=9.99...

10X-X=9

9X=9

X=1=0.99...

I don`t really think that proof is valid. You need to show why 10X-X=9. The person who doesn`t understand that .999... = 1 won`t really understand that the decimal portion of 10X equals the decimal portion of X.

X=0.99...

10X=9.99...

10X-X=9

9X=9

X=1=0.99..."

problem with this is that .99 x 10 is 9.90, not 9.99

3!=3*2*1=6

6!=6*5*so on and so forth.

And an easier way to get it wouldn`t be 120/6*2

Just do 5*4/2*1 (since you can cancel the 3*2*1)

Do you know what .99... means? It means that the 9 is repeating infinitely. You can`t say .99... *10= 9.90; that`s completely ignoring what the proof is telling you.

Anyways, I can`t believe you don`t believe that .99... is not 1. You can`t look at it differently; that`s the beauty of math: it`s straight-up true or not.

Wiki

If you are still arguing this, try taking a basic calculus course and then come talk.

"Here:

1. Legendre`s Constant

2. ???

3. Unicode HTML

4. Modular arithmetic

5. Golden Mean

6. Factorial 3

7. 6.99999...

8. Binary (1x2^3 + 0x2^2 + 0x2^1 + 0x2^0)

9. Base-4 (like Binary is Base 2 and Hex is Base 16, this is Base 4 numbering)

10. Binomial Coefficient

11. Hexadecimal

12. Cube root=inverse of 12^3

No idea on number 2."

2 is just summation notation for the infinite geometric sum of 1/2

We got them all. Very cool clock. I would pay money for this...

Don`t get me wrong, I`m not poking fun, I love this.

IAB is a complex community, with many undercurrents and subcultures...

AM or PM?

That was a lie.

I never took Algebra.