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# 2+2

Wed 28 Oct, 2009 07:25 am
I read somewhere that 2+2 does not equal 4 it is something like 3.99999.

What is this fella talking about? or was it a joke that I didn't see?
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Type: Question • Score: 1 • Views: 2,486 • Replies: 16

contrex

2
Wed 28 Oct, 2009 07:32 am
@lovejoy,
Take 2 items and put them on a table. Take 2 more and put them on the table. Now count all the items on the table. Now you know what 2+2 equals. The same as 1+1+1+1. Surely this is obvious?
0 Replies

2
Wed 28 Oct, 2009 07:39 am
@lovejoy,
It's an inside joke in math circles.

3.999999... (infinitely repeating) is actually equal to 4. There's a proof for this somewhere; what it boils down to is that there is no number between 3.99999 (infinitely repeating) and 4, so they must be the same number.

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contrex

1
Wed 28 Oct, 2009 08:32 am
Except that 3.999 (infinitely repeating) is an abstract concept and the integer 4 can be directly experienced.
ebrown p

2
Wed 28 Oct, 2009 09:03 am
@lovejoy,
Yes, it is a silly math diversion of the kind that the extremely nerdy among us use to entertain themselves.

I have also heard that 2+2 = 5 for extremely large values of 2.
0 Replies

1
Wed 28 Oct, 2009 10:33 am
@contrex,
I submit that conceptualizing 3.9999... is a more direct experience than your experiment of looking at four marbles.

One happens directly in one's brain, whereas looking at a physical object involves all sorts of distractions and distortions.
dyslexia

3
Wed 28 Oct, 2009 10:42 am

I submit that conceptualizing 3.9999... is a more direct experience than your experiment of looking at four marbles.

One happens directly in one's brain, whereas looking at a physical object involves all sorts of distractions and distortions.
well that would depend on whether the marbles were aggies, steelies or catseyes.
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contrex

1
Wed 28 Oct, 2009 12:50 pm
Quote:
I submit that conceptualizing 3.9999... is a more direct experience

I don't really see how you can assert that. Let's get rid of the 3 - it's an irrelevance, and just have 0.99999... I do understand that the number of 9s can be continued for as long as one pleases, and that the number thus expressed would approach 1 as closely as one pleases. But 0.9999... will always be an irrational number, and 1 will always be a rational number. The difference is fundamental, as Cantor observed.

I can imagine 1 perfectly easily, but imagining a quantity less than 1 but approaching it to an arbitrary degree of closeness is not something I can easily conjure up in my mind's eye.
oolongteasup

3
Wed 28 Oct, 2009 07:56 pm
@lovejoy,
1/3 x 12 = 4

1/3 = 0.3333333333 repeater

0.333333333 repeater x 12 = 3.999999999 repeater

therefore 3.99999999 repeater equals 4

qed
0 Replies

1
Wed 28 Oct, 2009 09:18 pm
@contrex,
That doesn't mean that other people can't conjure it up.

.9999... is 1.

1/3 = .3333333...

1/3 * 3= .3333333... * 3

1 = 0.9999999...

Q.E.D.
oolongteasup

2
Thu 29 Oct, 2009 02:22 am

whats that smell is it plagiarism
contrex

1
Thu 29 Oct, 2009 03:36 am
@oolongteasup,
Quote:
1/3 = 0.3333333333 repeater

You are using the concept of "equality" somewhat loosely.

one third, a perfectly respectable rational number, becomes a non-terminating decimal fraction. This is a consequence of decimal notation, not a "proof" that 0.99999.... "equals" 1.

1/3 + 1/3 + 1/3 = (1+1+1) / 3 = 1

1
Thu 29 Oct, 2009 07:10 am
@contrex,
Any repeating decimal is a rational number as well, so .9999... is a "perfectly respectable rational number".

Not sure where you're getting that I'm using "'equality'" loosely.

Here are a few examples:

No, I'm Sorry, It Does.

Quote:
.9 repeating equals one. In other words, .9999999... is the same number as 1. They're 2 different ways of writing the same number. Kind of like 1.5, 1 1/2, 3/2, and 99/66. All the same.

0 Replies

tsarstepan

1
Thu 29 Oct, 2009 07:27 am
@oolongteasup,
oolongteasup wrote:

whats that smell is it plagiarism

Plagiarist?! Plagiarist?! Where?! Where?!
Villagers rise and get the plagiarist!

1
Thu 29 Oct, 2009 07:34 am
@tsarstepan,
I'm afraid I'm a bit late in reading that since oolong's posts don't show for me. But my response is: How does one plagiarize a mathematical proof?
0 Replies

lovejoy

1
Mon 2 Nov, 2009 08:39 am
0 Replies

theplater

1
Tue 8 Dec, 2009 06:51 pm
A=0.999999 recursive define A
10A=9.999999 recursive multiply by 10
9A=9 substract A aka 0.9999rec
A=1 divide by 9
1=0.99999 recursive substitute in A from first statement
QED
0 Replies

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