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0 12 3 3 2 3 0 04 54 2 6, 5 22 7 2 6, 4 3, 6 4 / 5 6 2 38 / 69 / / 0 12 /8 0 1 6,,/ / 0 / 5 9 4 8 ;. To begin with, if F = á M, N, P ñ, then the divergence of F( x,y,z) is defined to be div F = M x N y P z Notice that the divergence of a vector field is a function and not a vector field Similarly, the curl of F( x,y,z) is defined to be the new vector field curl F = áP yN z, M zP x, N xM y ñ Equivalently, the curl of a vector field can be defined formally by curl F = Ñ×F. For any infinite sets x and P(x) (P(x) is the power set of x), if x < y < P(x), then either y=x or y=P(x) In other words, for any set x and its power set (P(x)), there is no set whose cardinality is strictly in between x and P(x) In the following pages we will demonstrate that the Generalized Continuum Hypothesis is consistent with the ZermeloFrankael axiom system That is, we will prove.

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@ a b c (/ d e a f g h i a j k a l m. That is, the 2form dF corresponds to the curl of the vector field F = á M, N, P ñ, so that Stoke's theorem in terms of differential forms is as follows Stoke's Theorem If F is a 1form with differentiable coefficients and S is an oriented surface, then ¶S F = ó õ ó õ S dF This general version of Stoke's theorem not only includes all the preceding statements of the fundamental. U B 7 6 á E » B X / v µ µ o ( u P µ v ( o W ~ K P ( } C u } v À À } o.

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F á dr ,whereC is oriented in the counterclockwise direction (when viewed from above the plane) FIGURE 25 Let F =!. X áy "# x ## y. P Ò o 4 i ¥ V r 4 * % ¥ å & J ' í & ) ¨ º ½ ¥ å g 4 z g 4 k A 9 ÷ = ª " # / V ¥ x q 4 4 k z x a j 4 ÿ Î Ä J è å J ) ( & f á × ò = e ¥ 4 q 4 i k x o z X Y T * G I ª *% ¥ K J ' I = K 3 2 W G 2.

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