Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**Roraborealis****Member**- Registered: 2005-03-17
- Posts: 1,594

My maths tutor told me this, and I'm very curious about it. Every time I try to follow it, I get confused. It apparently proves that 1=0.

x=1.

Multiply both sides by x and you get

2x=x

Take away 1 from each side which becomes

2x-1=x-1

This can also be expressed as

(x+1)+(x-1)=x-1

Divide each side by x-1 and the answer is:

x+1=1

From this, you can see that x=0. But at the beginning I said that x=1. It has therefore been proved that 1=0.

Is this a trick?

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,636

I know there IS something like this, but right at the start your tutor's proof says "2x=x" which can't be true (unless x=0 when lots of silly things become true).

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Offline

**Roraborealis****Member**- Registered: 2005-03-17
- Posts: 1,594

Aha. I knew it was a trick when I couldn't understand it!

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,636

But there is this one:

Start with: a = b

Then add (-b+b) to the left hand side (this is OK because you are adding 0: a - b + b = b

Now divide both sides by (a-b) and we have:

a - b + b = b

________ _____

(a-b) (a-b)

Reducing the left side:

1 + b = b

____ _____

(a-b) (a-b)

Then subtract b/(a-b) from both sides and you have:

1=0

(Mwuuhahhah - maniacal laughter!)

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Offline

**Roraborealis****Member**- Registered: 2005-03-17
- Posts: 1,594

Hahahahahaha! It's humorous to see that algebra can prove weird things!

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,636

But before we all think that Algebra is odd, there IS a mistake in the proof.

When I first saw it I was confooosed, and someone had to point out to me that because we said that a=b, then (a-b) must equal zero. When you start multiplying or dividing by zero, all hell breaks loose, and you start to get weird looking proofs.

So watch out for those in your proofs!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Offline

**Roraborealis****Member**- Registered: 2005-03-17
- Posts: 1,594

Oh.........never mind. At least it was funny.

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

Offline

**insomnia****Real Member**- Registered: 2005-03-23
- Posts: 944

That was weird. Any more like that?

Friends are angels who lift our feet when our own wings have trouble remembering how to fly

Offline

**austin81****Member**- Registered: 2005-03-21
- Posts: 39

It's not a trick! There's wrong division in the course of dividing both sides of the equation (x+1)+(x-1)=x-1 by x-1.

Offline

**Roraborealis****Member**- Registered: 2005-03-17
- Posts: 1,594

I do have another......

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

Offline

**Mr T****Member**- Registered: 2005-03-30
- Posts: 1,012

Go on then.

I come back stronger than a powered-up Pac-Man

I bought a large popcorn @ the cinema the other day, it was pretty big...some might even say it was "large

Fatboy Slim is a Legend

Offline

**konduriravali****Member**- Registered: 2005-04-09
- Posts: 17

Hi,

How are you doing?

By the way where do you stay.

Send me mail ,go to HELPME and then you go to

Maths by ravali.

byeeeee,

ravali

Offline

**Mr T****Member**- Registered: 2005-03-30
- Posts: 1,012

I am doing good.

I come back stronger than a powered-up Pac-Man

I bought a large popcorn @ the cinema the other day, it was pretty big...some might even say it was "large

Fatboy Slim is a Legend

Offline

**Roraborealis****Member**- Registered: 2005-03-17
- Posts: 1,594

I think most of us here are in the UK (well, I think, anyway).

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

Offline

**stewie****Member**- Registered: 2005-03-28
- Posts: 820

I'm actually living in Antarctica.

HAPPY HAPPY, JOY JOY

Fatboy Slim is the band of the 90s, thats if you want to call it a band because its really a one man name

Offline

**Mr T****Member**- Registered: 2005-03-30
- Posts: 1,012

That's because you have a thing for penguins.

I come back stronger than a powered-up Pac-Man

I bought a large popcorn @ the cinema the other day, it was pretty big...some might even say it was "large

Fatboy Slim is a Legend

Offline

**stewie****Member**- Registered: 2005-03-28
- Posts: 820

Actually my favourite animals are ducks. *quacks*

*Last edited by stewie (2005-04-14 08:13:15)*

HAPPY HAPPY, JOY JOY

Fatboy Slim is the band of the 90s, thats if you want to call it a band because its really a one man name

Offline

**stewie****Member**- Registered: 2005-03-28
- Posts: 820

I don't care. I know what I like and that's white white white.

HAPPY HAPPY, JOY JOY

Fatboy Slim is the band of the 90s, thats if you want to call it a band because its really a one man name

Offline

**Mr T****Member**- Registered: 2005-03-30
- Posts: 1,012

It's good for ye, top models eat it.

I bought a large popcorn @ the cinema the other day, it was pretty big...some might even say it was "large

Fatboy Slim is a Legend

Offline

**stewie****Member**- Registered: 2005-03-28
- Posts: 820

Give us grease that makes us obese....oh how we love to eat junk!

Fatboy Slim is the band of the 90s, thats if you want to call it a band because its really a one man name

Offline

**Mr T****Member**- Registered: 2005-03-30
- Posts: 1,012

Too far Tony, too far.

I bought a large popcorn @ the cinema the other day, it was pretty big...some might even say it was "large

Fatboy Slim is a Legend

Offline

**stewie****Member**- Registered: 2005-03-28
- Posts: 820

Whatever Trevor

Fatboy Slim is the band of the 90s, thats if you want to call it a band because its really a one man name

Offline

**Mr T****Member**- Registered: 2005-03-30
- Posts: 1,012

Yet again, my phrase, you stole it, check earlier topics again.

I bought a large popcorn @ the cinema the other day, it was pretty big...some might even say it was "large

Fatboy Slim is a Legend

Offline

**stewie****Member**- Registered: 2005-03-28
- Posts: 820

Actually no, you heard me saying it and put it in here before me!

Fatboy Slim is the band of the 90s, thats if you want to call it a band because its really a one man name

Offline

**Mr T****Member**- Registered: 2005-03-30
- Posts: 1,012

You came up with drinkin bleach, I'll give you that but I did not steal whatever Trevor off you foo'

I bought a large popcorn @ the cinema the other day, it was pretty big...some might even say it was "large

Fatboy Slim is a Legend

Offline