Truth and probability
Keynes in his A Treatise on Probability (1921) argued against the subjective approach in epistemic probabilities. For Keynes, subjectivity of probabilities doesn't matter as much, as for him there is an objective relationship between knowledge and probabilities, as knowledge is disembodied and not personal.
Ramsey in his article disagrees with Keynes's approach as for him there is a difference between the notions of probability in physics and in logic. For Ramsey probability is not related to a disembodied body of knowledge but is related to the knowledge that each individual possesses alone. Thus personal beliefs that are formulated by this individual knowledge govern probabilities, leading to the notions of subjective probability and Bayesian probability. Consequently, subjective probabilities can be inferred by observing actions that reflect individuals' personal beliefs. Ramsey argued that the degree of probability that an individual attaches to a particular outcome can be measured by finding what odds the individual would accept when betting on that outcome.
Ramsey suggested a way of deriving a consistent theory of choice under uncertainty that could isolate beliefs from preferences while still maintaining subjective probabilities.
Despite the fact that Ramsey's work on probabilities was of great importance again no one paid any attention to it until the publication of Theory of Games and Economic Behavior of John von Neumann and Oskar Morgenstern in 1944 (1947 2nd ed.)
ある数がほとんど整数（ほとんどせいすう、英: almost integer）であるとは、整数ではないが、整数に非常に近いことを意味する。どれほど近ければ十分であるのか明確な決まりはないが、一見して整数に近いとは分からないのに、近似値を計算すると驚くほど整数に近い数で、小数点以下の部分が「.000…」または「.999…」のように、0か9が数個連続する場合、このように表現される。例えば、「インドの魔術師」の異名をもつシュリニヴァーサ・ラマヌジャンは
65537 は {\displaystyle 2^{2^{4}}+1}2^{{2^{4}}}+1 の形で表され、2018年2月現在知られているうちで最大のフェルマー素数である。カール・フリードリヒ・ガウスは1801年に出版した『整数論の研究』において、p がフェルマー素数ならば正 p 角形は定規とコンパスで作図可能であることを証明した。また、逆に、奇素数 p に対して正 p 角形が作図可能ならば、p はフェルマー素数であることも証明した
