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cragar
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I can add 2 dense sets together and get a non dense set right?
cragar said:A dense set means its uncountable right?
cragar said:And uncountable meaning If I am at one number I couldn't tell you the next number in the list.
cragar said:Like the set of real numbers is uncountable . And I thought that means that if I am at 0 there is no next number to the right of zero on the continuum? Or am I wrong .
cragar said:so uncountable means that I can't put the set into a one-to-one correspondence with the natural numbers.
And are all uncountable sets infinite?
cragar said:If I excluded finite sets would that definition work.
And I am still not sure what a dense set is.
cragar said:Im not sure I understand you definition of dense . When you say a set D is dense in X, What is X is it a set,
and then you say x_n goes to x , Are you saying I can match up these elements?
cragar said:is x an element of D .
and when you say [itex] x_n [/itex] converges to x , is this like a limit ?
cragar said:All of my math background is applied math. calculus and differential equations. I am a physics major. I am taking discrete math this summer so maybe I should wait. My original question was can I have the union of 2 dense sets and get a non-dense set.
cragar said:I was reading a book called infinity and it talked about dense sets.
Could I have the union of 2 uncountable sets and make it a countable set.
cragar said:Is the smallest infinity the set of natural numbers?
cragar said:but aren't there an infinite number of positive even numbers which would be a subset of the naturals.
cragar said:ok and why can we say that there are more reals than naturals . I mean they are both infinite. I have seen cantors diagonal argument.
cragar said:Ok I see , I am very much enjoying this conversation .
Adding two dense sets for a non-dense set result refers to the mathematical operation of combining two sets that contain infinite elements in a way that results in a set with a finite number of elements.
This operation is important in mathematics because it allows us to work with infinite sets in a more manageable way. It also has applications in various fields such as analysis, topology, and number theory.
An example of this operation would be adding the set of all rational numbers (which is dense) to the set of all irrational numbers (also dense) to obtain the set of real numbers (which is non-dense).
No, not all combinations of dense sets will result in a non-dense set. For example, adding two dense sets of even numbers will still result in a dense set of even numbers.
Yes, there are various methods for adding two dense sets to obtain a non-dense set result, such as using the concept of limits or constructing a bijection between the two sets. The method used may depend on the specific sets being added and the desired result.