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While the proofs by infinite descent are constructively valid when "irrational" is defined to mean "not rational", we can obtain a constructively stronger statement by using a positive definition of "irrational" as "quantifiably apart from every rational". Let a and b be positive integers such that 1< a / b < 3/2 (as 1<2< 9/4 satisfies ...
A radical ideal is an ideal that equals its own radical. In a polynomial ring k [ x 1 , … , x n ] {\displaystyle k[x_{1},\ldots ,x_{n}]} over a field k , an ideal is radical if and only if it is the set of all polynomials that are zero on an affine algebraic set (this is a consequence of Hilbert's Nullstellensatz ).
Square roots of positive numbers are not in general rational numbers, and so cannot be written as a terminating or recurring decimal expression. Therefore in general any attempt to compute a square root expressed in decimal form can only yield an approximation, though a sequence of increasingly accurate approximations can be obtained.
In biology, parts of the DNA double helix that need to separate easily, such as the TATAAT Pribnow box in some promoters, tend to have a high AT content, making the strands easier to pull apart. [29] In the laboratory, the strength of this interaction can be measured by finding the melting temperature T m necessary to break half of the hydrogen ...
This aim of understanding the biochemistry of a cell reaches its most complex expression in the synthesis of huge amounts of enzyme kinetic and gene expression data into mathematical models of entire organisms. This is achievable in some well-studied bacteria, with models of Escherichia coli metabolism now being produced and tested.
The history of scientific method considers changes in the methodology of scientific inquiry, not the history of science itself. The development of rules for scientific reasoning has not been straightforward; scientific method has been the subject of intense and recurring debate throughout the history of science, and eminent natural philosophers and scientists have argued for the primacy of ...
This shift in preference from terms highlighting biological sex ("transsexual", "FtM") to terms highlighting gender identity and expression ("transgender", "trans man") reflects a broader shift in the understanding of transgender people's sense of self and the increasing recognition of those who decline medical reassignment as part of the ...
Burning Man is a week-long large-scale desert event focused on "community, art, self-expression, and self-reliance" held annually in the western United States. [1] [2] The event's name comes from its culminating ceremony: the symbolic burning of a large wooden effigy, referred to as the Man, that occurs on the penultimate night, the Saturday evening before Labor Day. [3]