I thought math was always logical?

[pirana 0]

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It says that 3.99999999999999999. . . . is basically equal to four. It's not 100% correct; the bar over the 9 is an approximation and does not represent a real representable integer, so the equals sign is really an "approximately equals" sign.

Ask any mathemaetician worth their weight in chalk dust and it is an equals sign; not a congruency, not approximately equals; but equals.

.9 repetend 9 does equal 1.

Not intuitive to normal thinking, but then a lot of math past Algebra and Geometry isn't.

" . . . the lust for power can be just as completely satisfied by suggesting people into loving their servitude as by flogging them and kicking them into obedience." -- Aldous Huxley

[carmenc 0]

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Factoring error.

(a+b)(a-b) is not a square minus b square.

(a+b)(a-b) = a^2 -ab +ab -b^2 = a^2 - b^2

[georgerussia 0]

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so 3.999999 .... = 4?

It may be, depending on application.

If you're doing 2D draws, it definitely is - you basically draw on integer axis, and you cannot plot at 3.9 - either 3 or 4.

Even on DirectX/OpenGL 3D, which supports float coordinates and texture mapping, the difference even between 3.99 and 4.00 is negligible unless your system of coordinates is in 3.95 - 4.00 range. In those applications 3.99999.... = 4.

* Don't pray for me if you wanna help - just send me a check. *

[MiataMan 0]

The proof is wrong.

3.(bar)9 is equal to 3 + (infinty-1)/(infinity)

However,

39.(bar)9 does not equal 3(10) + (infinity-1)(10)/(infinity).

Infinity is a conceptual math. Infinity is not to be used in algebraic math.

Proof would be:

x = 3.(bar)9
y = 0.(bar)9

x = 3+y

(10)x = (10)3+(10)y
10x-x = (10)3+(10)y-(3+y)
9x=(9)3+(9)(y)
9x/9=(27)/9+9y/9
x=3+y
x=3.(bar)9

A man without a mustache is like a hamburger without a bun, Un-American.

[jcd11235 0]

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It says that 3.99999999999999999. . . . is basically equal to four. It's not 100% correct; the bar over the 9 is an approximation and does not represent a real representable integer, so the equals sign is really an "approximately equals" sign.

Actually, it is 100% correct. There are many ways to prove that 0.999…999… is exactly equal to 1.

Math tutoring available. Only $6! per hour! First lesson: Factorials!

[jcd11235 0]

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That's nothing...check this out:

Let...

a=1
b=1

That means

a=b

multiply both sides by a
a2 = ab

Subtact b2 from both sides
a2 - b2 = ab - b2
Factor

(a+b)(a-b) = b(a-b)

Divide both sides by (a-b)
*crosses out both (a-b)*

a+b=b

If
a=1 and b=1

Then
1+1=1
2=1

Dividing by zero is an undefined operation. Your conclusion is therefor unjustified.

Edit: Shropshire beat me to it.

Math tutoring available. Only $6! per hour! First lesson: Factorials!

[champu 1]

So a man walks into the "Infinite Inn" which is a hotel with an infinite number of rooms. He walks up to the clerk and asks if he's got any rooms available and the clerk says, "Nope, we're all full up."

Then the clerk thinks for a minute and says, "Wait, I've got an idea!" He picks up the PA and says, "Attention everyone in the hotel. Sorry for the inconvienience, but I have to ask everyone to please step out of your room, note your room number, and please go to one room number higher than yours."

All of the hotel guests comply and once the terrible racket of doors opening and closing settles down the clerk turns back to the man and says, "We've got one room available. Room number 1, first door on the left."

The man says, "well actually I need more than one room. I need a room for myself and for each of my children, and their children, and so on extending back infinitely up my family tree." To which the clerk replies, "well I'm afraid I can't help you, you'll have to try Aleph Suites next door."

[champu 1]

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And I thought that Speaker's Corner was supposed to be about Guns, Gays, or God.]

math is sounding more and more like a religion to me. The answer depends on who you ask and many say it is semantic game, while others insist they are right and the others are wrong.

Forgot to add .. some will insult you when you don't understand their version.

btw, religion and mathematics (particularly set theory of cardinalities greater than aleph0) do have something in common. Studying either in great detail can lead you to believe you've unlocked deep and meaningful secrets of the universe when all you've really done is wrapped yourself around the axle of a construct created by man as a means to communicate ideas.

Physics on the other hand...

[kallend 2,027]

Aleph-naught bottles of beer on the wall,
Aleph-naught bottles of beer,
Take one down, and pass it around,
Aleph-naught bottles of beer on the wall
(repeat forever).

...

The only sure way to survive a canopy collision is not to have one.

[lewmonst 0]

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It says that 3.99999999999999999. . . . is basically equal to four. It's not 100% correct; the bar over the 9 is an approximation and does not represent a real representable integer, so the equals sign is really an "approximately equals" sign.

This thread is hilarious. Thanks for the laugh everyone.

Bill, seriously, "approximation"? I'm losing faith in you. It's not an approximation, it's a repeating decimal equal to 1.

.9 repeating = 1

so YES, 3.9(repeating 9) = 4

and 2.349999999... = 2.35

I teach 12 year-olds this, they get it.

There are several proofs and useful discussions here: http://en.wikipedia.org/wiki/0.999...

My favorite:
"Q: How many mathematicians does it take to screw in a lightbulb?

A: 0.999999…."

hahahahahaha(repeating "ha")...

Karen

http://www.exitshot.com

[kallend 2,027]

So why is 0! = 1 ?

...

The only sure way to survive a canopy collision is not to have one.

[champu 1]

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So why is 0! = 1 ?

Convenience.

[SivaGanesha 2]

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There are several proofs and useful discussions here: http://en.wikipedia.org/wiki/0.999...

Can you summarize what is on that page? I haven't been able to finish typing in the URL yet...

"It's hard to have fun at 4-way unless your whole team gets down to the ground safely to do it again!"--Northern California Skydiving League re USPA Safety Day, March 8, 2014

[likearock 2]

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So why is 0! = 1 ?

To satisfy the recurrence relation:

(n+1)! = n! * (n+1)

[kallend 2,027]

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So why is 0! = 1 ?

To satisfy the recurrence relation:

(n+1)! = n! * (n+1)

How Convenient. Pity about n=-1 isn't it?

1 used to be a prime number when I was in school. Then mathematicians found it more convenient to say that it wasn't prime. Funny how fashions change.

...

The only sure way to survive a canopy collision is not to have one.

[pirana 0]

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Factoring error.

(a+b)(a-b) is not a square minus b square.

(a+b)(a-b) = a^2 -ab +ab -b^2 = a^2 - b^2

My bad. I had not seen that little puzzle in a long time and jumped too quickly.

" . . . the lust for power can be just as completely satisfied by suggesting people into loving their servitude as by flogging them and kicking them into obedience." -- Aldous Huxley

[pirana 0]

Here's a fun little one to puzzle over.

" . . . the lust for power can be just as completely satisfied by suggesting people into loving their servitude as by flogging them and kicking them into obedience." -- Aldous Huxley

[FreeflyChile 0]

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Here's a fun little one to puzzle over.

Well for one the slope of the hypotenuse of the green triangle is not the same as the slope of the hypotenuse of the red triangle, so the two large triangles are not identical.

[shropshire 0]

I reckon that you're right. The ratios (opposite : adjacent) are different 0.375 for the red and 0.4 for the green ..... the bottom left angles are different.

(.)Y(.)
Chivalry is not dead; it only sleeps for want of work to do. - Jerome K Jerome

[kallend 2,027]

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Here's a fun little one to puzzle over.

Well for one the slope of the hypotenuse of the green triangle is not the same as the slope of the hypotenuse of the red triangle, so the two large triangles are not identical.

So the big "triangle" in the top picture is not really a triangle at all, since its "hypotenuse" is not a straight line.

...

The only sure way to survive a canopy collision is not to have one.

[FreeflyChile 0]

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Here's a fun little one to puzzle over.

Well for one the slope of the hypotenuse of the green triangle is not the same as the slope of the hypotenuse of the red triangle, so the two large triangles are not identical.

So the big "triangle" in the top picture is not really a triangle at all, since its "hypotenuse" is not a straight line.

My excuse for the lack of terminology is that English is my second language...

[kallend 2,027]

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Here's a fun little one to puzzle over.

Well for one the slope of the hypotenuse of the green triangle is not the same as the slope of the hypotenuse of the red triangle, so the two large triangles are not identical.

So the big "triangle" in the top picture is not really a triangle at all, since its "hypotenuse" is not a straight line.

My excuse for the lack of terminology is that English is my second language...

Unfortunate indeed, but we can't hold you personally responsible for that shortcoming.

...

The only sure way to survive a canopy collision is not to have one.

[likearock 2]

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Here's a fun little one to puzzle over.

Well for one the slope of the hypotenuse of the green triangle is not the same as the slope of the hypotenuse of the red triangle, so the two large triangles are not identical.

So the big "triangle" in the top picture is not really a triangle at all, since its "hypotenuse" is not a straight line.

Neither big "triangle", top or bottom, is a triangle for that same reason.

[shropshire 0]

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Neither big "triangle", top or bottom, is a triangle for that same reason.

I think that you'll find that they are triangles (provided all the sides are straight lines)... They are just not 'Similar Triangles' (same shape, different size)

(.)Y(.)
Chivalry is not dead; it only sleeps for want of work to do. - Jerome K Jerome

[likearock 2]

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Neither big "triangle", top or bottom, is a triangle for that same reason.

I think that you'll find that they are triangles (provided all the sides are straight lines)... They are just not 'Similar Triangles' (same shape, different size)

The point is neither hypotenuse is a straight line.

To see this, compare the slopes of the more acute angles of the red and dark green triangles.

Red: 3/8 = .375
Green: 2/5 = .4

If you did a sine calculation, you would find that the smallest angle in the red triangle was more acute than the smallest angle in the green. Any way you line them up, you can never get a straight line.

But that, of course, is the reason for the missing box.