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The weakness of this intelligent design supporting book is the fact that its estimates of probabilities for synchronicities, are very rough: the book is focused on finding indefinite patterns (so called "law of near enough" - events are similar but not strictly identical [55]) for small group of people but in very loosely defined vast amount of ...
The real numbers can be defined synthetically as an ordered field satisfying some version of the completeness axiom.Different versions of this axiom are all equivalent in the sense that any ordered field that satisfies one form of completeness satisfies all of them, apart from Cauchy completeness and nested intervals theorem, which are strictly weaker in that there are non Archimedean fields ...
The long real line pastes together ℵ 1 * + ℵ 1 copies of the real line plus a single point (here ℵ 1 * denotes the reversed ordering of ℵ 1) to create an ordered set that is "locally" identical to the real numbers, but somehow longer; for instance, there is an order-preserving embedding of ℵ 1 in the long real line but not in the real ...
Just thinking about synchronicities made me realize, I’m surrounded by them. ... 22 10-minute breakfast recipes you'll want to make forever. Food. Eating Well. 17 new anti-inflammatory dinners ...
The operations make the real numbers a field, and, along with the order, an ordered field. The real number system is the unique complete ordered field, in the sense that any other complete ordered field is isomorphic to it. Intuitively, completeness means that there are no 'gaps' (or 'holes') in the real numbers.
If the number of trials were increased to 10,000, the probability of it happening at least once in 10,000 trials rises to ( 1 − 0.999 10000 ≈ 0.99995, or ) 99.995%. In other words, a highly unlikely event, given enough independent trials with some fixed number of draws per trial, is even more likely to occur.
Also, someone who could do a 360 flip on a skateboard and make the perfect cappuccino (I was in my youth and folly; my expectations were low). Little did I know I was manifesting a person to enter ...
An axiomatic definition of the real numbers consists of defining them as the elements of a complete ordered field. [2] [3] [4] This means the following: The real numbers form a set, commonly denoted , containing two distinguished elements denoted 0 and 1, and on which are defined two binary operations and one binary relation; the operations are called addition and multiplication of real ...