It is exact. Look at 22/7 as an approximation to pi. We used it in elementary school and middle school. It is very close and a repeating decimal fraction: 3.142857 142857 142857 …. Now look at |pi – 22/7| / pi. What we have is an error of 0.000402499 or, about 0.04% Very close. Similarly, for the Euler-Mascheroni constant gamma, 0.577215665…, we see that Sqrt(3)/3 is 0.577350269… and the error is |gamma – 1/Sqrt(3)| / gamma = 0.000233196, or about 0.02% or thereabouts. Taunus Trumbo: And so what? These are transcendental numbers being approximated by rational numbers or algebraic irrationals (surds). Faustus Mortal: They establish a numerical criterion. For anything in the physical universe, a good approximation must have an error less than these. Taunus Trumbo: And this proves? Faustus Mortal: The error in A+1/A+B and e^(pi^2/2) is 0.000000146 or 0.00001%. Even the absolute error is small, 0.000020. Taunus Trumbo: This is a remarkable coincidence, but little more. Faustus. "We could do it properly," his grip on my wrists slackening slightly."But you're with Eddie," he said."No we split out today," I lied, "look no engagement ring."He looked up I bent my finger slightly to let him see. I was gambling nowbut I had nothing to lose my head moving forward my tongue snaked intohis ear whispering."You know some quality time together, take a lot longer time for a bitmuscular guy like you to make me squeal with delight," as my mouth movedtowards his opening as I spoke meeting his lips my tongue moving betweenthem as I kissed him he responded at first then stopped."Nice try," he said, "but I've got a reputation to think of you know meGordy with a someone who changes sex, don't think so, you see this way Iget my fun and nobody knows just like William did," my breath caught inmy throat."Yeah that's right I know about his little visit, sick fuck phoned me totell me all about it thought it might get him into my good bookssomehow." The words had just left his mouth.
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