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In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), is defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways. [1] The most famous taxicab number is 1729 = Ta(2) = 1 3 + 12 3 = 9 3 + 10 3 , also known as the Hardy-Ramanujan number.
1 (one, unit, unity) is a number, numeral, and glyph.It is the first and smallest positive integer of the infinite sequence of natural numbers.This fundamental property has led to its unique uses in other fields, ranging from science to sports, where it commonly denotes the first, leading, or top thing in a group. 1 is the unit of counting or measurement, a determiner for singular nouns, and a ...
A 16-bit number can distinguish 65536 different possibilities. For example, unsigned binary notation exhausts all possible 16-bit codes in uniquely identifying the numbers 0 to 65535. In this scheme, 65536 is the least natural number that can not be represented with 16 bits. Conversely, it is the "first" or smallest positive integer that ...
For example, the smallest positive number that can be represented in binary64 is 2 −1074; contributions to the −1074 figure include the emin value −1022 and all but one of the 53 significand bits (2 −1022 − (53 − 1) = 2 −1074). Decimal digits is the precision of the format expressed in terms of an equivalent number of decimal digits.
The smallest number with full precision is 1000...0 2 (106 zeros) × 2 −1074, or 1.000...0 2 (106 zeros) × 2 −968. Numbers whose magnitude is smaller than 2 −1021 will not have additional precision compared with double precision. The actual number of bits of precision can vary.
Here we can show how to convert a base-10 real number into an IEEE 754 binary32 format using the following outline: Consider a real number with an integer and a fraction part such as 12.375; Convert and normalize the integer part into binary; Convert the fraction part using the following technique as shown here
As a result the smallest number of h possible will give a more erroneous approximation of a derivative than a somewhat larger number. This is perhaps the most common and serious accuracy problem. Conversions to integer are not intuitive: converting (63.0/9.0) to integer yields 7, but converting (0.63/0.09) may yield 6.
The Berry paradox is a self-referential paradox arising from an expression like "The smallest positive integer not definable in under sixty letters" (a phrase with fifty-seven letters). Bertrand Russell , the first to discuss the paradox in print, attributed it to G. G. Berry (1867–1928), [ 1 ] a junior librarian at Oxford 's Bodleian Library .