2 + 2 = 5

[Brad Barker]

interesting side note: one of my friends used perfectly logical mathematical stuff to 'prove' that 1=2. A calculus professor couldn't find anything wrong with his math.

you divide by zero at one point. the trick is to dress it up really fancy so that it's not obvious if you haven't been paying attention.


...or you could just be looking at a set where every element is 0 (i.e., satisfies the property of zero: x+0=0).

 

[CrazyArcher]

Yep, most of those tricks are build on dividong by zero. This way, you get infinity, so it means that 1 is really far from 2, which perfectly makes sense.
BTW, if the professor doesn't see an error there - he shouldn't teach Seriously enough, I think everyone past 1st year of undergraduate studies must know this trick.

 

[morf]

No, no, no, 0.999999 with an infinite number of 9's does not equal 1, but it roughly equals (that squiggly equal sign) to 1. 0.9999999 is 0.9999999, 1 is 1.
Also that infinite hotel problem is a brain twister... It's pretty much there's a hotel with infinite number of rooms, and each room is filled with a guest, and 5 new guests came to the hotel, and they took the first 5 rooms, and other guests each moved down 5 rooms, will there be enough rooms? That's not as philosophical as the 0.999 IMO.

3/3 = 1, and thus 1/3 + 1/3 + 1/3 equals exactly 1.

it saying that 1/3 = 0.3333 thats incorrect, because 1/3 = 0.3333 (3 repeating) ONLY IF 3 x 1/3 = exactly 1.

 

[BoneMachine]

It really is false to say that 2+2=4 always. This depends largely on the module of the arithmetic at use. Modular arithmetics can give rise to blatantly 'false' statements, as judged by our usual everyday mathematical usage. One good example is -3 = 2 (mod 5).

 

[Diggler]

NERDS!!!!
[Invalid or Expired Link Removed]

...and this is coming from a computer programmer.

 

[morf]

NERDS!!!!
[Invalid or Expired Link Removed]

...and this is coming from a computer programmer.

A picture of major metal before the KGB had him cut his hair?

 

[funkydjembe]

I would say that "1/3" is a perfect number. The problem is in our decimal system. If we counted by thirds than 1/3 would be "1". Everything IS perfectly dividable by all numbers. It's like when you change the speed of music, it's still on time, it's just being divided from a different vantage point. We think in "tens" because it's practical (except for some who still like the "bushel" and "gallon" and "inch")

 

[bkim]

the problem is that 0.99999999... (9, repeating) is EXACTLY equal to 1!

your little example is a decent heuristic way to see it, but let's do it a little more rigorously.

suppose 0.9, with the 9 repeating infinitely, is a number.

let x = 0.9, with the 9 repeating.

consider 10*x:

10*x = 9.9, with the 9 repeating.

now consider 10*x - x:

9.9 (9 repeating) - 0.9 (9 repeating) = 9.

so we have...

9*x = 9.

thus x=1.

but x WAS 0.9 (9 repeating).

so the two numbers are the same.


this has to do something with "the completeness of real numbers," although i don't like math NEARLY enough to read anything about it.

1*1=1
1*1*1*1*1=1
x=.999999........
x*x does not =x
x*x*x*x*x*x does not =x
.9999999999.......does not =1

 

[Brad Barker]

1*1=1
1*1*1*1*1=1
x=.999999........
x*x does not =x
x*x*x*x*x*x does not =x
.9999999999.......does not =1

your "proof" isn't good at all. your fourth line requires quite a bit more work (as it stands, you just make an unjustified claim and let it be), and after you do that work, you will see that x*x is indeed the same as 1*1.

try working through my proof on your own, referring to it as needed.

or maybe working through another example that's easier to swallow will help:

HOW TO WRITE "0.3 (3 repeated)" AS A FRACTION:

let x=0.3 (3 repeated)

consider 10*x: 3.3 (3 repeated).

now consider 10*x - x: 3.

so 9*x = 3.

dividing, we have x=3/9, or x=1/3.


...i hope that you can at least buy that.

 

[Poop-Loops]

1*1=1
1*1*1*1*1=1
x=.999999........
x*x does not =x

Then what does it equal?

0.99....8

So you have an infinite amount of 9's, and then an 8.

Meaning you have an infinite amount of 9's. You never actually get to the 8.

So it's just 0.999......

Hooray!

The best way it was explained to me is Brad's proof and also the way my prof. explained it:

If 0.999.... and 1 are two different numbers, then there must be a number in between the two. What is it?

 

[bkim]

Then what does it equal?

0.99....8

So you have an infinite amount of 9's, and then an 8.

No, you have an infinite amount of 9's, and it ends in a 1

 

[mactac]

i will prove that 2 + 2 =5:

I dare you to find the mistake.

assume the variable a & the variable b.
assume that a=b

so, we get
a=b
a^2=ab (multiply both sides by a)
a^2 - b^2 = ab-b^2 (subtract b^2)
(a+b)(a-b)=b(a-b) (factor)
a+b=b (divide both sides by (a-b)
b+b=b (since a=b)
2b=b
2=1 (divide both sides by b)

since 2=1, and 5=2+2+1, we could also say that 5=1+2+1
which is equal to:
5=2+2

there you have it.


*NOTE**** if you have seen this before & know the "trick" don't tell... let some people squirm over it for a while

 

[funkydjembe]

This stuff is like "crossing a river to search for water". 1 is one, and only 1 no matter how large or small 1 is. 2+2=5, all you have to do is change the value of 2. Or 5. what is 5?

 

[Obese Chess]

you divide by zero at one point. the trick is to dress it up really fancy so that it's not obvious if you haven't been paying attention.


...or you could just be looking at a set where every element is 0 (i.e., satisfies the property of zero: x+0=0).

no, but, it was like, nothing weird...I forget how he did it

fun note: "you haven't been paying attention" is the chorus of the Radiohead song "2+2=5"

 

[morf]

The mistake is assuming that either variable = 1 to begin with.

 

[mactac]

The mistake is assuming that either variable = 1 to begin with.

no I didn't.


..and either way, it wouldn't matter anyways. a variable is a variable & can stand for anything. but, as I mentioned, there is no such assumption in my proof

 

[neptoon]

consider cutting a pie into thirds...after you've cut the pie into thirds, look at your knife...there's your rogue 0.00000(infinite)1...the whole pie isn't there in the pie pan...i've always been fond of my ability to take pi out to all of the decimal points simply by saying 22/7...numbers suck...

 

[morf]

since 2=1, and 5=2+2+1, we could also say that 5=1+2+1

Here you assume that in 5=2+2+1 the variable 2 is equal to 1. Just like you assume the solution to the previous problem, 2=1, applies to calculating 5.

 

[mactac]

consider cutting a pie into thirds...after you've cut the pie into thirds, look at your knife...there's your rogue 0.00000(infinite)1...the whole pie isn't there in the pie pan...i've always been fond of my ability to take pi out to all of the decimal points simply by saying 22/7...numbers suck...

pi does not equal 22/7. not even close.

 

[mactac]

0.9 (repeated) equals *exactly* 1.

0.0000(repeated forever)...1 equals *exactly* zero. it never gets to the 1 at the end.

This is a principle that is well understood by mathematicians. It's only laypeople that end up having this debate.

you need to fully grasp the idea of infinity to understand it. the zeros go *forever*. the 1 on the end is not relevant.