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# Do all infinite sets are equivalent sets?

Updated: 4/27/2022

Wiki User

10y ago

we can consider all infinite sets as equivlent sets if we go by the the cantor set theory.for eg. on a number line if we consider the nos. between 0 and 1 as a set then they are infinite. similarly the nos. between 0 and 5 can also be considered infinite and if considered as a set then they can be considered as equivalent

Wiki User

10y ago

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Q: Do all infinite sets are equivalent sets?
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### What are the equivalents sets?

Equivalent sets are sets that have the same cardinality. For finite sets it means that they have the same number of distinct elements.For infinite sets, though, things get a bit complicated. Then it is possible for a set to be equivalent to a proper subset of itself: for example, the set of all integers is equivalent to the set of all even integers. What is required is a one-to-one mapping, f(x) = 2x, from the first set to the second.

Absolutely not

### What is the kinds of sets?

Closed sets and open sets, or finite and infinite sets.

### What are kind of set?

There are finite sets, countably infinite sets and uncountably infinite sets.

### What is equavalit set?

I assume the question is meant to be about equivalent sets. Two sets are said to be equivalent if they have the same cardinality. For finite sets, it means that they must both have the same number of distinct elements. More generally, two sets are equivalent if (and only if) there exists a one-to-one mapping (bijection) from one set to the other. This definition applies to equivalence of infinite sets but does give rise to some counter-intuitive results. For example, the set of all integers is equivalent to its proper subset, the set of all odd integers. The mapping for all to evens is x-&gt; 2x.

### Are all equivalent sets are equal sets?

Yes. Equivalent means equal.

### Kinds of sets and its example?

Sets are collection of distinct objects. In mathematics there are different types of sets like Finite set, Infinite set, Universal set, subset, equal set, equivalent set. Example of Finite set {1,2,3,4}. Infinite set:{1,2,3....}.

### Can you name all the sets of numbers to which 15 belongs to?

The number 15 belongs to an infinite amount of sets.

### What are three examples of infinite sets?

stars in the sky that's the some example of infinite sets

Yes.

### Are equivalent sets equal sets why?

No, because equivalent sets are sets that have the SAME cardinality but equal sets are sets that all their elements are precisely the SAME. example: A={a,b,c} and B={1,2,3} equivalent sets C={1,2,3} and D={1,2,3} equal sets

### What is the two kind of sets?

Closed sets and open sets, or finite and infinite sets.