2+2

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?

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.

Except that 3.999 (infinitely repeating) is an abstract concept and the integer 4 can be directly experienced.

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.

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.

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.

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

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.

bit late dad

whats that smell is it plagiarism

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

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.

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

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?

I now wish I hadn't asked

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