Solve both with explanation A correspondence is a 1-1 and onto function. 18. Wri

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Solve both with explanation

A correspondence is a 1-1 and onto function. 18. Write down a correspondence between [2,4,6,8,10 and the integers strictly between -50 and -56 19. Write down a correspondence between the positive natural numbers N+ = {1,2,3, ) and (0k11 kand I are odd positive integers } = the collection of all finite strings s of 0's and l's where s is an odd number of O's followed by an odd number of 1's. For this problem you can be a bit informal and indicate the correspondence f by ordering the binary string in the set and letting f(1) the first element in the ordered set, f(2) = the 2nd element in the ordered set, etc.

Explanation / Answer

There is no one-to-one correspondence between N and P(N)

a correspondance between the {2,4,6,8,10} and the intergers strictly beween -50 and -56

An integer value is typically specified in the source code of a program as a sequence of digits optionally prefixed with + or . Some programming languages allow other notations, such as hexadecimal (base 16) or octal (base 8). Some programming languages also permit digit group separators.[2]

The internal representation of this datum is the way the value is stored in the computer's memory. Unlike mathematical integers, a typical datum in a computer has some minimal and maximum possible value.

The most common representation of a positive integer is a string of bits, using the binary numeral system. The order of the memory bytes storing the bits varies; see endianness. The width or precision of an integral type is the number of bits in its representation. An integral type with n bits can encode 2n numbers; for example an unsigned type typically represents the non-negative values 0 through 2n1. Other encodings of integer values to bit patterns are sometimes used, for example binary-coded decimal or Gray code, or as printed character codes such as ASCII.

There are four well-known ways to represent signed numbers in a binary computing system. The most common is two's complement, which allows a signed integral type with n bits to represent numbers from 2(n1) through 2(n1)1.

Two's complement arithmetic is convenient because there is a perfect one-to-one correspondence between representations and values (in particular, no separate +0 and 0), and because addition, subtraction and multiplication do not need to distinguish between signed and unsigned types. Other possibilities include offset binary, sign-magnitude, and ones' complement.

19)

Every composite number can be a value of a slope-intercept equation for a straight line. For the interval between two perfect squares, x2x2 and (x+1)2(x+1)2, the size of the set of intersecting slopes is equal to (x+1)2(x+1)2.

The linear equations are of the standard form y=mz+by=mz+b where the intercept is double the slope (b=2mb=2m). By definition, mm is a factor - prime or composite - of yy. Of a set, the smallest mm is x+1x+1 and the largest mm is (x+1)23(x+1)23.

There are no other slopes required to intersect every nonprime number in the interval with the exception of semiprimes divisible by 22 - that is, yy = bb.

the slopes for which mm is even. Of interest are odd-mm slopes that intersect odd and even numbers where the value of yycan only be even within a perfect square interval. Where mm is odd, the value of yy is the same parity as zz. Therefore: for z=0z=0, yyis even (y=by=b); for z=1z=1, yy is odd (y=m+by=m+b); for z=2z=2, yy is even (y=2m+by=2m+b). Every interval greater than {36,49}{36,49} has at least two slopes where: for z=1z=1, y<x2y<x2; for z=2z=2, y>x2y>x2 and <(x+1)2<(x+1)2; for z=3z=3, y>(x+1)2y>(x+1)2.

Equivalently, there are at least two composites of the form 22m22m where mm is odd. Notice that an odd-2m2m slope can cross just one number in the interval. An odd-mm slope can have two yy values (odd and even) only if it has variables zz and z+1z+1 where z>x2z>x2.

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