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# Maths illusions watch

1. (Original post by sherunsaway)
Moron. You can't divide both by (b-a) because there isn't a (b-a) on each side. Look carefully on the right side and there is (a+b) and (a-b), neither of which is the same as (b-a). All this example proves is how good your eyesight is.
(Original post by MR_JR)
^^

thus his proof is incorrect
Here you go. both of you, i corrected my equation. I wrote it correctly on paper, but just typed it incorrectly here (seems more prone to mistyping maths on computer!!!). i apologise for the inconvenience.
2. ^^
no worry. It wasnt a dig at you, but the person who started with "oh it is right"

now its corrected, tis funkeh
3. (Original post by MR_JR)
^^
no worry. It wasnt a dig at you, but the person who started with "oh it is right"

now its corrected, tis funkeh
cheers.

[btw ppl wondering how it is possible - the divide by (b-a) is wrong, as if a=b, therefore b-a=0, and you can't divide by 0! but most people dont notice!]
4. (Original post by dvs)
-1 = -1
1/-1 = -1/1
sqrt(1/-1) = sqrt(-1/1)
1/i = i/1
1 = i^2
1 = -1

problem here "sqrt(1/-1) = sqrt(-1/1)"

when you sqrt a negative fraction, the numerator (top bit) always becomes the negative. So square rooting 1/-1 or -1/1 always returns i/1.

if your calculator can be put into complex mode, try putting in 1/i, it probably will give you an error.

i think thats right.
5. (Original post by Zuber)
cheers.

[btw ppl wondering how it is possible - the divide by (b-a) is wrong, as if a=b, therefore b-a=0, and you can't divide by 0! but most people dont notice!]
you can always divide by 0!
6. (Original post by phreek)
problem here "sqrt(1/-1) = sqrt(-1/1)"

when you sqrt a negative fraction, the numerator (top bit) always becomes the negative. So square rooting 1/-1 or -1/1 always returns i/1.

if your calculator can be put into complex mode, try putting in 1/i, it probably will give you an error.

i think thats right.
no, it's just people forget that -1 has two squareroots, +/- i
7. (Original post by homoterror)
no, it's just people forget that -1 has two squareroots, +/- i
i thought about that, but that applies for √1 too, so you'd have both sides as + or -
8. (Original post by phreek)
i thought about that, but that applies for root √1 too, so you'd have both sides as + or -
yes that is obvious.

9. it's like b x 0 = a x 0 = 0 where u can replace a and b with whatever u like ....
10. here's one (which may have already been posted, i admit i haven't looked)

1/4 > 1/8
(1/2)² > (1/2)³
log (1/2)² > log (1/2)³
2 log(1/2) > 3 log(1/2)
2 > 3

QED

lol, its easy enough to figure it out but its quite neat
11. (Original post by MC REN)
here's one (which may have already been posted, i admit i haven't looked)

1/4 > 1/8
(1/2)² > (1/2)³
log (1/2)² > log (1/2)³
2 log(1/2) > 3 log(1/2)
2 > 3

QED

lol, its easy enough to figure it out but its quite neat

Is it just my browser or do the TeX fonts look really awful on this forum?

no, it's just people forget that -1 has two squareroots, +/- i
Don't we define ?
though has the two solutions
12. (Original post by Gaz031)

Is it just my browser or do the TeX fonts look really awful on this forum?
yer, well done
13. I really feel an urge to shoot whoever it was that revived this thread
14. a glass with a capacity of 1 litre has 0.5 litres in it - ppl often say it is either half empty of half full and that pessimists choose half empty and optimists choose half full

'the glass is half empty' FALSE

an empty glass has 0 litres inside

half of empty is 0.5 x 0 = 0 which doesn't equal 0.5

'the glass is half full' TRUE

a full glass has 1 litre in it

half full is 0.5 x 1 = 500mml

therefore a 1 litre glass with 0.5litres in it is not half empty, but half full
15. What would appease you?

Half Drained?
16. (Original post by esx77)
a glass with a capacity of 1 litre has 0.5 litres in it - ppl often say it is either half empty of half full and that pessimists choose half empty and optimists choose half full

'the glass is half empty' FALSE

an empty glass has 0 litres inside

half of empty is 0.5 x 0 = 0 which doesn't equal 0.5

'the glass is half full' TRUE

a full glass has 1 litre in it

half full is 0.5 x 1 = 500mml

therefore a 1 litre glass with 0.5litres in it is not half empty, but half full
im one of them dumb ones i just realized. But it still makes sense doesnt it?
17. (Original post by MR_JR)
its wrong. You cant divide.....

DAMNIT sherunsaway you beat me to it!!!!

Old classic

x=0.9reccuring
*10
10x=9.9 reccuring
10x-x
9x=9
x=1

But x also equals 1, meaning that 1 ≡ 0.9reccuring

Im thinking though, could this have the same principle as an ordered pair, in that to fit the quation there are 2 possible values. Actually maybe not, as they dont proooveeach other. Hmm i dunno
dude. 1 is 0.9 recurring.
18. Wrong.

However infinately small the differencee between 0.9rec and 1, there IS a difference. In this case it would be like

0.01 with an infinite number of zeros
19. (Original post by MR_JR)
Wrong.

However infinately small the differencee between 0.9rec and 1, there IS a difference. In this case it would be like

0.01 with an infinite number of zeros
No there isn't.
There's no such thing as 0.00....(rec).....1. You can't have any number after this infinite number of zeros.
0.9rec and 1 are one and the same. (notice the unintentional but amusing pun there!)
20. Yes indeed 0.9rec = 0 + 9/10*(1+1/10+1/10^2....+1/10^n) as n tends to infinity

You can recognise the sum of a geometric serie:

1+1/10+ 1/10^2.....+1/10^n = 1/(1-1/10) = 10/9 (as n tends to infinity)

Hence 0.9rec = 9/10*10/9 = 1 qed

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