1=1?

[Missing the point]

LOL


I think 1 = 1 only when 2 = 2, and only then does 0 = 0, and produced from that is 3 = 3, and 2 = 3, multiplied by 4 = 2, and 1 = 1 is the square root, so that can be divided to come to the conclusion that 1 = 1.5, so yes, they are not equal

[rtyp3]

I saw somewhere some equation thing that shows that 1 doesn't equal 1. Anyone know what I'm talking about? If they do, can you tell me what it was.

[alpha]

Yep! 1 does not equal 1, least not according to my Pentium F0.

[medo]

Hello


?????

I am lost.

Medo

http://sysopt.earthweb.com/forum/smile.gif

[hd581]

I found this on another UBB:

x = y
x^2 = xy
x^2 - y^2 = xy - y^2
(x+y)(x-y) = y(x-y)
x+y = y
Since x = y, y + y = y
2y = y
Divide by y, 2 = 1.and this:
i^2 = -1
i * i = -1
sqrt(-1) * sqrt(-1) = -1
sqrt(-1 * -1) = -1
sqrt(1) = -1
1 = -1



[This message has been edited by hd581 (edited 05-25-2000).]

[chipbgt]

there is a mathematical flaw in those equations that trics people into thinking its a true statement. see if you can find it.

[hd581]

I actually had to dust off my algebra book for the second one.

[rtyp3]

chip- are you talking about the square root of a negative number, in this case, 1?

[Mr. Mojo Risin]

actually the square root of negative 1 = i although thats not the topic at hand.

[Ollie Cook]

The proof is OK up to here:


(x+y)(x-y) = y(x-y)


but you cannot make the following step

x+y = y


because (x-y) = 0 and it is therefore division by zero - which is not allowed.

Ollie

[alpha]

Ok, just do the equation on your Pentium F0 - 1 = 0.999945255479842234538876 - It's so simple!!

[ILC]

Headache now.

[GregM]

While we are messing with the rules of math -
1/9 = 0.11111...
2/9 = 0.22222...
.
.
.
9/9 = 0.99999... = 1
Therefor, 1 is infinitesimally smaller than one. Or, 1=9/9 1-9/9 >0 1-1 >0 So 1 doesn't equal one, least not in the world of finite precision.

[mourikise]

rtyp3, you don't make clear where you saw that equation. Actually, if you talk about computers, alpha is right. But if you saw it on a book about maths then the answer is surely most complicated! For example the chaos theory accepts that universe is an analog machine so it is prety unlikely to find number 1 in the nature. It 's more common to find 1.00000000000000000000123 or 1.0000037 but to simplify things an electric engineer or a physician will mark both values as 1, which practically is absolutely correct! I think that's what GregM wants to demonstrate with his example. Also, it is possible this equation to comes from the field of mathematical analysis. Please, provide more info on where you saw the equation so that I can search more specifically and try to find some bibliography about this topic.

[mourikise]

Just some corrections.
To hd581:

As Ollie Cook mentioned you can never divide by zero (x=y => x-y=0). Also, we should make clear that i is a number which its square equals -1. That's the definition of i. This doesn't give us the right to talk about sqrt(i), since sqrt is a function for real numbers only, not fantastic ones.

To GregM:

As you correctly mention 1/9 = 0.11111... But there is no mathematical rule according to which you can devide 2,3,4,....,9 using the same method. What I want to say is that till 8/9 you are going just fine, but not because you are replacing the 1s with 2s,3s,4s,...,8s ,respectively, in the number 0.11111... but because if you do make the calculations by hand you will end to these results. So, 9/9 actually epuals exactly 1 (9 fits 9 exactly 1 time, as our schoolteacher used to tell us).

I hate pretending the smart guy; all I want to do is help the conversation. If I 'm wrong or I didn't understand what you actually ment let me know.

[krusty the klown]

x = y
x^2 = xy
x^2 - y^2 = xy - y^2
(x+y)(x-y) = y(x-y)
x+y = y
Since x = y, y + y = y
2y = y
Divide by y, 2 = 1.

is flawed at the line (x+y)(x-y) = y(x-y)

(x+y)(x-y) = x^2 + yx - xy -y^2
= x^2 -y^2, which is not equal to y(x-y)

[hd581]

mourikise, I know it's hard to see it clearly since we're in a text-only medium, but I was merely converting i to its square root notation: sqrt(-1), not taking the sqrt of an imaginary number.

If it helps, use j (as physicists do). j^2 = -1
j * j = -1
sqrt(-1) * sqrt(-1) = -1
sqrt(-1 * -1) = -1
sqrt(1) = -1
1 = -1


[This message has been edited by hd581 (edited 06-01-2000).]

[rtyp3]

I saw it at the letters section at www.dailyradar.com (http://www.dailyradar.com) a few months ago... thats about all I remember. I'll go back and see if I can find it again.

[GregM]

mourikise, you are right. You can get there (not correctly) by saying 1/9 = 0.111... so 9*1/9 = 0.999..., which you could by a series. Of course I was not being serious, but didn't think the discussion was very serious, with division by zero, etc.

[GregM]

mourikise, you are right. I could show a series to demonstrate it, though:
1/9 = 0.111...
9 * 1/9 = 0.999... = 9/9 = 1. The series would be 9 * 1/9 = 9*0.1 + 9*0.01 + 9*0.001 ...
I know that is not a mathematical proof. I wasn't being serious. I didn't think the thread was too serious with division by zero and other indeterminates and identity errors. Should we disprove Fermat's last theorem next?

[ScaryBinary]

I once figured out if there were any non-zero integer solutions to the equation x^n + y^n = z^n for values of n greater than 2. I didn't have enough paper to document my proof, though, so I just jotted myself a note in the margin of a book I had laying around.

Now I can't find my actual proof!

ScaryBinary

[alpha]

Mouriske:
Actually, I was just slaggin' intel and the Pentium - familiar with the F0 bug?? Made things like 2 x 2 = 3.999986622344901 http://sysopt.earthweb.com/forum/smile.gif

[krusty the klown]

Produces
Erroneous
Numbers
Through
Incompetent
Understanding of
Mathematics

[hd581]

sqrt(-1) * sqrt(-1) = -1
sqrt(-1 * -1) = -1
The rule sqrt(a)*sqrt(b) = sqrt(a*b) only holds true for positive numbers.

[Evil Knievel]

Pretty smart there you guys. <<big frown>> You're all overlooking the fact that square rooting something actually produces two results.

1^2=1
-1^2=1

Therefor:
sqrt(1)=1,-1

Don't any of you remember your 10th grade quadratics!?


Your friendly neighborhood hacker/motocrosser
Joel Sullivan
p.livingstone@ns.sympatico.ca

[blind to truth]

umm

[BFlurie]

Good one Krusty -- I always wondered where PENTIUM came from.

[rtyp3]

How about this:
Begin with a=b.

So a-b+b=b. Dividing both sides by (a-b) we get (a-b+b)/(a-b) = b/(a-b). Simplifying, we get 1+b/(a-b) = b/(a-b). Subtracting b/(a-b) from both sides, we end up with 1 = 0

Is their something I am overlooking?

[This message has been edited by rtyp3 (edited 06-27-2000).]

[danthanol]

Rtyp3:

If a=b, a-b = 0. You cannot divide by a-b.

There is also an error in your simplifying step, if you sidestep what's above...

(a-b+b)/(a-b)=b/(a-b)
a-b = 0, so...
b/(a-b) = b/(a-b)
1=1

[Ghost Rider]

"There can be only one!"

[800XL]

Who's on first again?

Most of these types of equations abuse either divide by zero or multiples of infinity, which for this purpose are basically the same thing. (0 goes into any number as many times as you care to try to make it). 1*infinity=2*infinity, divide out the infinities and you get 1=2.

[Bak]

I would just like to take this oppertunity to say I have been a proud amiga user for a long time, now I use PeeCeez i am proud to say i have a processor that doesn't guess answers to summz, it just works dem out, why cannot intel just make a processor that works out stuff quickly instead of estimating the answer (yes i know it can be patched)

Has anyone a mathematical equation the AMD K6-2/66 cannot work out propperly to prove im wrong? I would like to take this oppertunity to ask all people to semi-ignore my post entirely.

Ok, im happy now

YOU CAN NOW RESUME RAMBLING ON ABOUT STUFF
(**** capslock)

[MAGIC 8-BALL and THE ELF]

I'm 1. Are you 1 too? If so 1 is not equal to 1. - 8-Ball

1 is the lonliest number, they say, even worse if it's not =1. - Elf

[Konan555]

If you understood Radiohead you'd know

"1=2 we hope that you choke"

[fritzp]

I am going to have to take the high road
3=1 if you put away the algebra book and pick up the good book you will find this is the case and 1=all #

Fred

[RaeRae]

Can anyone explain the story of the people who went to a hotel...I've never been able to find the reason for the inequality???

I can't remember the story now either... it was something like 3 guys went to a hotel and paid a certain amount, then a refund was given so the hotel manager went to give them the refund and gave each one something back, and kept a little or something ... and well the numbers did not add back up to the original sum... ****, any help would be appreciated :-)

Thanks!

[Konan555]

It's somthing like:

3 Guys go to shop and pay £5 each for somthing. The manager tells the shop asistant to give them back £5 but the asistant pockets £2 and gives them back £3 (£1 each)

So...

they paid £4 each (£12) the asistant's got £2 (£14) - where's the other pound?

[cmagnusson]

It's all explained by quantum physics.

[Worm]

There actually was something that stated 1 <> 1 I forget what is was, but I will say... numbers are relative. A number is non-existent, therefore they all = {} No number can exist because your base "0" does not exist. Nothing would have to be a something to name it nothing or... 0. If zero were something then it would be 1 not 0. Without a basis for comparison you connot have the latter. If 0 had to be one, 2 could not mean 2, 3 would actually have to be 2, making 0 now 2 instead of 1, therefore you 2 objects would then become 4, and zero 3. It is a paradox. Therfore 1 does not always equal one.
Worm

[conroy]

----------------------------------
3 Guys go to shop and pay £5 each for somthing. The manager tells the shop asistant to give them back £5 but the asistant pockets £2 and gives them back £3 (£1 each)

So...

they paid £4 each (£12) the asistant's got £2 (£14) - where's the other pound?
-----------------------------------

This problem has puzzled me too, but a few months ago I found a site to explain it (and all OTHER math paradoxes)

just go to:
http://forum.swarthmore.edu/dr.math/problems/moran2.26.96.html

-Mary

[Evil Knievel]

The Pentiums don't guess or estimate the answers! Geez! =)
All the stuff that you guys were talking about earlier is because computers use logarithms to get their answers.
That's why 2*2 = nearly 4.

[FIZZICS CHICK]

To Mourikise:
"It 's more common to find 1.00000000000000000000123 or 1.0000037 but to
simplify things an electric engineer or a physician will mark both values as 1..."

I disagree. I think it is us who complicate things. For example, we might say that a proton weighs 6.27*10^-31 kg, but does nature really care what we label her proton with? It really is just a proton. But then again, that is an oversimplification of an amazingly complex tiny little machine.