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The only assumption we made was that log 2 3 is rational (and so expressible as a quotient of integers m/n with n ≠ 0). The contradiction means that this assumption must be false, i.e. log 2 3 is irrational, and can never be expressed as a quotient of integers m/n with n ≠ 0. Cases such as log 10 2 can be treated similarly. Types
Predictably Irrational: The Hidden Forces That Shape Our Decisions is a 2008 book by Dan Ariely, in which he challenges readers' assumptions about making decisions based on rational thought. Ariely explains, "My goal, by the end of this book, is to help you fundamentally rethink what makes you and the people around you tick.
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator p and a non-zero denominator q. [1] For example, is a rational number, as is every integer (e.g., ). The set of all rational numbers, also referred to as " the rationals ", [2] the field of rationals [3 ...
A typical Dedekind cut of the rational numbers is given by the partition (,) with = {: < <}, = {:}. This cut represents the irrational number in Dedekind's construction. The essential idea is that we use a set , which is the set of all rational numbers whose squares are less than 2, to "represent" number , and further, by defining properly arithmetic operators over these sets (addition ...
If you’re a first-time homebuyer feeling worried by the 20% down payment guidance commonly quoted, know that a down payment can actually be much lower—for example, 3% to 5% depending on loan type.
Stocks ticked lower from their intraday highs when the forecast was released, but the S&P 500 still closed above 5,400 for the first time ever, while the Nasdaq Composite rallied more than 1.5% to ...
The former president focused on a 20% rate but also mentioned 15%, a number he has pushed for previously. Trump liked the 20% level, according to the CEO, in part because it was a "round number."
In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
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