Question

5-8 please

Consider the following dozen infinite sets comparisons. Write down >, < or = between each pair of sets to indicate their relative size. SET #1 SET #2 1: {1,2,3,4,...} all natural numbers) The natural numbers starting with 3] {3,4,5,6,...} {1,2,3,4,...} (all natural numbers) (All even natural numbers] {2,4,6,8,...} {1,2,3,4,...} all natural numbers All odd natural numbers) {1,3,5,7,...} {1,2,3,4,...} (all natural numbers] All unit fractions) {1,1/2, 1/3,1/4,...} {1,2,3,4,...} (all natural numbers) All points on an infinite line] (All points on a finite line segment All points on an infinite line) 7: {1,3,5,7,...) all odd natural numbers (All multiples of four) {4,8,12,16...} 8: {10,20,30,40,...} (all multiples of 10 (All multiples of four) {4,8,12,16...) [All points on an infinite line) [All points on a line 1" long) 10 [All points inside a unit circle [All points on the circumference of a unit circle 11: (All points inside a unit circle All points inside a unit square (All points on a line 1/2" long) (All points on a line 1" long) 12

Answer 1

{1,2,3 ... } (Natural Numbers) are - Countably infinite , where as all perents on an infinito line are uncountably infinite => {1,2,3---} < All fornito con empiride line 6 Sine , number of points on a finite line segment on an infinite line are both un- Conntably infinite So, size of these sets is [Ale points on a finite line seg. ] = {All fite on an inf. hire ] Same i.e. # All odd numbers are countably infinite and also all multiple of 4 are countably infinito . => [Ale odd numbers] - [ Ale multiple of 4 ] odd & - => All mutiples of 10 are countably infinite and all multiples of 4 are also countably infinite [All multiples of lo] =[All multiples of 4].