where can I find the proof that (-1)(-1)=1?
365423
This proof is trivial. The number -1 is defined as the number satisfying the equation 1 + (-1) = (-1) + 1 = 0. \nMultiply both sides by -1:\n(-1)*1 + (-1)*(-1) = 0\nby the distributive property.\nBy the fact that 1 is the multiplicative identity and the definition of additive inverse, we get:\n-1 + (-1)*(-1) = 1 + (-1)\nAdd 1 to both sides (additive inverse property):\n(-1)*(-1) = 1.\nQED.
619728
The problem is between step 5 and step 6.\n a(a - b - 1) = b(a - b - 1) \ncan not be reduced to a=b, because if a-b-1=0, you can't divide both side with it. \nAnd in this case, indeed a-b-1=0.
775741
I cannot prove it formally but I can mention the steps\n\na | u(n)\n\na | u(n+1)\n\nso a | u(n+1) - u(n) if a devided b and a devided c then it devides b-c\n\nso a | u(n-1)\n\nthere by we reach a | u(0) and a|u(1)\n\nu(0) does not give any infomation as u(0) =0\n\nso a | u(1) = 1\nso a= +/-1 \nu(0) = 0\nu(1)  = 1\n\nnext terms are u(2) = 1,u(3) = 2 ,u(4) = 3, then 5,8,13,
211910
(-3)-[(-2)-(4)(-5)] \n(-3)-[(-2)-(-20)]\n(-3)-[-2+20]\n(-3)-18\n-21
792641
There's got to be additional information to the problem...\n\n(-1,-4) is simply a coordinate point on a plane.  \n-1=x coordinate\n-4=y coordinate\n\nhowever, if the problem is a proof then the statement is false because 9(-1)+3(-4)= -21 ...not 8
10571
50 is right.\n{i^2 -(-1)^i | i=1,2,...}
846663
(x+3)(x-1)\n\n x= -3\nx=1
206636
for (i=1,t=1,cosx=1;i<=n;++i)\n{\n  t=(-1)*(t*x*x)/((2*i)*(2*i-1);\n  cosx += t;\n}
874355
Using matices to do this\n\n[ 1 -2 1] * [x] = [-5]\n[ 2 -1 1]   [y]    [ 1]\n[2  1  2]   [z]    [10]\n\nAX = B\nA*A^(-1)X = A^(-1)B\nX = A^(-1)B\n\nSO we need the inverse of A this can be worked out using a long and tedious method or just use a calculator\n\nA^-1 = [ -.6 1 -.2]\n           [ -.4 0   2]   \n           [.8   -1 .6]\n\nA^-1B = [2}\n              [4}\n              [1]\nso x =2  y=4 z=1\n\n now you do the other one\nCheck\n2 - (4*2) +1 = 2 - 8 +1 = -5
902613
I just plugged this into my calculator.\n\n[1, 0, 2, 0, 2, 0 | 0\n0, 1, -3, 0, -2, 0 | 0\n0, 0, 0, 1, -1, 0 | 0\n0, 0, 0, 0, 0, 1 | 0\n0, 0, 0, 0, 0, 0 | 1 ]\n\nTake it however you want.
786717
its 1\n\nsince i = (-1)^1/2\n\nso i^2 = (-1)^(2*(1/2))\n\nwhich is 1
670743
There is no square root of -1.
577215
This again is a direct theorem from the field axioms: http://mathworld.wolfram.com/FieldAxioms.html . \nSuppose a*b = 0. If a is non-zero, multiply both sides by a^(-1) to get a^(-1)ab = a^(-1)0, and thus b = 0, since the product of 0 and any number is 0.\nIf b is non-zero, multiply both sides by b^(-1) to get the similar result a = 0. Thus, either b or a must be 0. \nThe final case is that both a and b are 0, which is trivial.\nFurther discussion of this theorem can be found in the source.\nThis theorem can be used to solve equations by getting 0 on one side of the equation and factoring the other side completely, then using the theorem to imply that at least one of the factors must be zero. For example, x^2 = -3x - 2 can be rearranged to be x^2 + 3x + 2 = 0. We factor the left side to read (x + 1)(x + 2) = 0. From the theorem we know that either x + 1 = 0 or x + 2 = 0 or both. Thus we have two solutions, x = -1 or x = -2. It is obvious that in this case, only one factor could be 0.
491468
If by x1/2 you mean x^(1/2), and by -1-[x] you mean -1 minus the absolute value of x, then the composite function f o g is (-1-[x])^(1/2).\n\nWhat is unusual about this is that this function is not defined for any real number x.  The expression (-1-[x]) is always going to be negative, no matter what x is.  Raising this to the power of 1/2 is the same as taking the square root of it.  Since the square root of a negative number is not defined in the real number system, the domain is the empty set.
947331
(-1/4)(16/4) (16)\n-1 * 16\n-16\nReciprocal = -[1/16]
904826
f(g(x)) = g(x) + 1 = (x^2 - 1) + 1 = x^2  - 1 + 1 = x^2\n\ng(f(x)) = (f(x))^2 - 1 = ( x + 1 )^2 - 1 = (x^2 + 2x + 1) - 1 \n                                                         = x^2 + 2x + 1 - 1 \n                                                          = x^2 + 2x
877357
#1\n\nt=0 or -3\n\n#2\n\np^2 - (1/4)^2 which is p^2 - 1/16