User:Arseniiv/Three-gap theorem: Difference between revisions
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:: Because of the Claim 2, one of the old steps projects into a step of another old size and into one of those intervals, which depends on if its genspan was negative or positive (equivalently, if it sat on a lower or upper diagonal). | :: Because of the Claim 2, one of the old steps projects into a step of another old size and into one of those intervals, which depends on if its genspan was negative or positive (equivalently, if it sat on a lower or upper diagonal). | ||
: '''CLAIM 3b''': That means if new steps aren't the same size, that one is a new size. | : '''CLAIM 3b''': That means if new steps aren't the same size, that one is a new size. | ||
:: '' | :: For now, a meh proof from contradiction: if the new steps are unequal and both happened before, then there should've been steps of both sizes in a scale one generator less, but there's also a third step size that was just split, so there were three step sizes in that scale, whereas we postulated just two. | ||