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No, the size of infinities vary! Some are smaller than others.
Eg: the size of the set of numbers between 0 and 1 is infinite (0.1,0.11 and so on), but the size of this infinity is different from the size of the set of all numbers.
This is very very complicated maths and even the greatest mathematicians have avoided this paradox.
I don't know the proof well so just search around the net for it.
In mathematics, there are at least two categories of infinite sets - countably infinite, and uncountably infinite. Countably infinite means that you can set up a one to one correspondence between all members of the set and the set of natural number, aka "counting numbers".
Integers are countably infinite. You can pair them up with the natural numbers thus: 1,0 2,-1 3,1 4,-2 5,2 6,-3 and so on. The set of even numbers, odd number, and rational numbers are all countably infinite. The set of Real numbers, however is uncountably infinite. It can be shown that you can identify at least one real number that is not included in the set when you try to count all real numbers - thus while there are an infinite number of integers, there are even MORE real numbers. Not all infinite sets have the same number of elements.
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What is the relationship of number of elements to number of subset?
A finite set, with n elements has 2n subsets, including the empty set and itself. For infinite sets the number of subsets is the same order of infinity.
What are the finite or infinite sets?
A finite set is one containing a finite number of distinct elements. The elements can be put into a 1-to-1 relationship with a proper subset of counting numbers. An infinite set is one which contains an infinite number of elements.
What is the meaning of equivalent set?
Equivalent sets are sets with exactly the same number of elements.
What are the different kinds of sets?
empty set- set contains no element EX. A= set of cosmonauts land on mars A( it is a null set because there are no cosmonauts land s on mars finite set- sets whose elements are countable EX. A ( a,e,i,o,u) there are four (4) it is countable infinite set- sets whose elements are uncountable EX. A. (1234......... and so on) has no end equal sets- sets with the same element EX. A( 1,2,3,4,5) B( 1,2,3,4,5) they have the both same element equivalent set- sets with the same number of elements ( note: number not element) EX. F ( a,b,c,d,e,f) they have both quantity in each set Q( 1,2,3,4,5) universal sets- total of all the elements on given sets (give the totality) EX. F( 1,2,3,4,5,) E(,6,7,8,9,10) total (1,2,3,4,5,6,7,8,9,10)
What are the different kinds of set operations?
empty set- set contains no element EX. A= set of cosmonauts land on mars A( it is a null set because there are no cosmonauts land s on mars finite set- sets whose elements are countable EX. A ( a,e,i,o,u) there are four (4) it is countable infinite set- sets whose elements are uncountable EX. A. (1234......... and so on) has no end equal sets- sets with the same element EX. A( 1,2,3,4,5) B( 1,2,3,4,5) they have the both same element equivalent set- sets with the same number of elements ( note: number not element) EX. F ( a,b,c,d,e,f) they have both quantity in each set Q( 1,2,3,4,5) universal sets- total of all the elements on given sets (give the totality) EX. F( 1,2,3,4,5,) E(,6,7,8,9,10) total (1,2,3,4,5,6,7,8,9,10)
