1. Dyadic fractions, explained above, unfortunately have limited use in a society based around decimal figures.
2. This group of definitions is dyadic fractions; a wider universe is reachable given some form of transfinite induction.
3. For example, the dyadic fractions are the localization of the ring of integers with respect to the powers of two.
4. In mathematics, more specifically in harmonic analysis, "'Walsh functions "'form a dyadic fractions.
5. When " y " is a dyadic fraction, the power function, may be composed from multiplication, multiplicative inverse and square root, all of which can be defined inductively.
6. It's difficult to find dyadic fraction in a sentence.
7. Fractions can be stored natively in a binary format by having each finger represent a fractional power of two : \ tfrac { 1 } { 2 ^ x } . ( These are known as dyadic fractions .)
8. A simple non-dyadic fraction such as 1 / 3 can be approximated as 341 / 1024 ( 0.3330078125 ), but the conversion between dyadic and vulgar ( 1 / 3 ) forms is complicated.
9. This set is nowhere dense, as it is closed and has an empty interior : any interval ( a, b ) is not contained in the set since the dyadic fractions in ( a, b ) have been removed.
10. No individual " S n " is closed under addition and multiplication ( except " S " 0 ), but " S " * is; it is the subring of the rationals consisting of all dyadic fractions.
11. The maximal subset of " S " ? that is closed under ( finite series of ) arithmetic operations is the field of real numbers, obtained by leaving out the infinities 鄙, the infinitesimals 钡, and the infinitesimal neighbors " y " 钡 of each nonzero dyadic fraction " y ".
12. The international standard symbol for inch is "'in "'( see ISO 31-1, Annex A ) but traditionally the inch is denoted by a dyadic fractions with odd number numerators; for example, would be written as & Prime; and not as 2.375 & Prime; nor as & Prime;.
13. This construction of the real numbers differs from the Dedekind cuts of standard analysis in that it starts from dyadic fractions rather than general rationals and naturally identifies each dyadic fraction in " S " ? with its forms in previous generations . ( The ?-complete forms of real elements of " S " ? are in one-to-one correspondence with the reals obtained by Dedekind cuts, under the proviso that Dedekind reals corresponding to rational numbers are represented by the form in which the cut point is omitted from both left and right sets . ) The rationals are not an identifiable stage in the surreal construction; they are merely the subset " Q " of " S " ? containing all elements " x " such that " x " " b " = " a " for some " a " and some nonzero " b ", both drawn from " S " *.
14. This construction of the real numbers differs from the Dedekind cuts of standard analysis in that it starts from dyadic fractions rather than general rationals and naturally identifies each dyadic fraction in " S " ? with its forms in previous generations . ( The ?-complete forms of real elements of " S " ? are in one-to-one correspondence with the reals obtained by Dedekind cuts, under the proviso that Dedekind reals corresponding to rational numbers are represented by the form in which the cut point is omitted from both left and right sets . ) The rationals are not an identifiable stage in the surreal construction; they are merely the subset " Q " of " S " ? containing all elements " x " such that " x " " b " = " a " for some " a " and some nonzero " b ", both drawn from " S " *.

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