16 Sep 07
Originally posted by EinsteinMindBut by rationalising it away you've changed the definition of SQRT to such an extent that the step 2->3 is no longer valid.
This convention will not work when x is any negative integer. for instance, the two square roots of -1 are indeed i and -i. These cannot be distinguished on the basis of "positive" and "negative"; so how do we know which one is being meant by SQRT -1?
Therefore this step of the proof may seem unclear.
HOwever, this can be easily remedied.
Just ...[text shortened]... ative multiple of i."
It simply rationalizes away by defining which SQRT you are after.
18 Sep 07
Originally posted by Doctor Rati'm seriously confused now...
If there is a general formula involved in the proof, make sure division by zero isn't happening because that isn't allowed. So for example the classic case of the fallacy of 1=2 (which is very similar to yours)
step 1
[b]Let a = b
step 2 Multiply both sides by a:
aa = ab
step 3 which is the same as:
a^2 = ...[text shortened]... oof of 2+2=5.
(sorry for all the edits, but I had to work out some formatting issues)
18 Sep 07
2 edits
step 1a^2 = ab
Let a = b
step 2 Multiply both sides by a:
aa = ab
step 3 which is the same as:
a^2 = ab ( "a squared equals a times b" )
step 4 Add the quantity ( a^2 - 2ab) to both sides:
a^2 + (a^2 - 2ab) = ab + (a^2 - 2ab)
step 5 simplifying both sides we get:
(a^2 + a^2) - 2ab = a^2 + (ab - 2ab)
2(a^2) - 2ab = a^2 - ab
2 (a^2 - ab) = a^2 - ab
step 6 divide both sides by (a^2 - ab):
2(a^2 ...[text shortened]... ab) / (a^2 - ab) = (a^2 - ab) / (a^2 -ab)
step 7 cancel out like terms in num.&denom:
2 = 1 !!!
then is a^2-ab = 0
devide by 0 is not allowed
18 Sep 07
Originally posted by EinsteinMindBut you are creating exactly this kind of ambiguity.
Wrong. It's a mistake, but an asusmption or a definition of which SQRT you are after, and the problem continues.
1) -1 = -1 check
2) sqrt(-1) = sqrt(-1) check (providing your rule)
3) ambiguity inserts itself....
4) i / 1 = 1 / i is i = -i wrong!
18 Sep 07
2 edits
Originally posted by eatmybishopYou will find that computers wouldn't convert to decimal, do the addition, and then convert back to binary. Decimal is only for us to easily understand, which is base 10 (ten) numbers. Binary are base two numbers which is what computers do arithmetic in because it can only handle two states.
tell me in what way that is wrong and i'll back down.... i sense you know you've lost....
here's the quote on binary numeral system...
could you actually read the whole thread then get back to me... if you have trouble understanding it send me a message and i'll explain it to you...
it is them who have converted the answer to decimal... 10 + 10 ur; it is not, its value remains 10"
is this wrong too????
apology accepted loser
Therefore, as far as computers is concerned, 1 + 1 = 0 (with 1 as a carry bit). Effectively meaning 01 + 01 = 10.
So if you were to do any addition in binary, it is quite correct to say 1 + 1 = 10. Same as saying 9 + 1 = 10 (decimal or base ten), or 7 + 1 = 10 (octal or base 8).
EDIT: What you are referring to is boolean algebra where "+" is representing the logic AND, which is something completely different.
0 AND 0 = 0
1 AND 0 = 0
0 AND 1 = 0
1 AND 1 = 1
20 Sep 07
Originally posted by lauseyit was actually me who said a computer will not convert to decimal... they were saying it would....
You will find that computers wouldn't convert to decimal, do the addition, and then convert back to binary. Decimal is only for us to easily understand, which is base 10 (ten) numbers. Binary are base two numbers which is what computers do arithmetic in because it can only handle two states.
Therefore, as far as computers is concerned, 1 + 1 = 0 (wi ...[text shortened]... hich is something completely different.
0 AND 0 = 0
1 AND 0 = 0
0 AND 1 = 0
1 AND 1 = 1
with all respect, your boolean algebra is incorrect.. it should read...
0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 1
hope this helps
20 Sep 07
Originally posted by eatmybishopEverything you post about binary is wrong. Just stop.
it was actually me who said a computer will not convert to decimal... they were saying it would....
with all respect, your boolean algebra is incorrect.. it should read...
0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 1
hope this helps