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The free group F S with free generating set S can be constructed as follows. S is a set of symbols, and we suppose for every s in S there is a corresponding "inverse" symbol, s −1, in a set S −1. Let T = S ∪ S −1, and define a word in S to be any written product of elements of T. That is, a word in S is an element of the monoid ...
A letter of thanks, letter of gratitude, thank you card, or thank you letter is a letter or greetings card that is used when one person/party wishes to express appreciation to another. They are frequently sent after an event (a birthday party, a religious festival or holiday) and especially when a gift has been received. [ 1 ]
In a 1954 paper, Strachey gave one of just a few extant examples of the kinds of love letter the program would generate: Darling Sweetheart, You are my avid fellow feeling. My affection curiously clings to your passionate wish. My liking yearns for your heart. You are my wistful sympathy: my tender liking. Yours beautifully M. U. C.
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The free group G = π 1 (X) has n = 2 generators corresponding to loops a,b from the base point P in X.The subgroup H of even-length words, with index e = [G : H] = 2, corresponds to the covering graph Y with two vertices corresponding to the cosets H and H' = aH = bH = a −1 H = b − 1 H, and two lifted edges for each of the original loop-edges a,b.
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Since its conception in 1994 by Judith Donath, [2] [3] the technology behind the E-card has changed significantly. One technical aspect that remained mostly constant until 2019 was the delivery mechanism: the e-mail received by the recipient contains not the E-card itself, but an individually coded link back to the publisher's website that displays the sender's card.