![]() ![]() ![]() ![]() The size of Q is equal to the dimension size of G. Since nW - nQ is not zero, there are words within W that cannot be in Q due to the contrains of G W contains more words than G can hold. With all generality, we can see that nQ = 2. Let d, be any word composed from the altered diagonal construction d = 10. Let W, be the paragraph of all possible combinations of words of length 2 nW = 2^2 ![]() Proof by induction that these properties hold for all paragraphs. T naturally becomes a sentence of all words not written in Q - which is all the words that could not be used in G. As a consequence, the intersection of Q with T is empty. Therefore, d is in T, d is in W but does is not in Q. Show that for any word, d, it is written in the sentence T, written in the sentence W, but not written in the sentence Q.ĭ = 1. Let T, be the sentence of all the words in W that are not in Q nT = nW - nQ = 2-1 = 1 With all generality, we can see that nQ = 1. Let Q, be the sentence composed of the words used in G and, ordered according to the rows in G. Let d, be any word composed from the altered diagonal construction d = 1. Let G, be a grid whose dimensions correspond to the word length in W. Let W, be the paragraph of all possible combinations of words of length 1 nW = 2^1 nB = 2, note: this is the smallest size alphabet which allows us to have a choice when construction an altered diagonal We will use this to construct words to build sentences and paragraphs from. An example of such an encoding is Kuratowski's definition of ordered pair, $(a,b) = \. The idea is that every statement that mathematicians care about is equivalent to some question about sets. But we can use $\sf ZFC$ as a foundation for all of mathematics by encoding the various other objects we care about in terms of sets. Sets are the only fundamental objects in the theory $\sf ZFC$. Oscar Cunningham Asks: Could groups be used instead of sets as a foundation of mathematics? ![]()
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