How Do You Express a Sequence Using Set Builder Notation?

It's just that it's not really a question, so I was wondering if there was something else you were looking for. But if you're just looking for confirmation, then that's fine. In summary, the notation for the set ##\{ ... , -8 , -3 , 2 , 7 , 12 , 17 ,...\}## is ##\{ \ 2+5y \ | \ y \in \mathbb{Z} \ \}## where ##2+5y## can be replaced by any element in the set.
  • #1
reenmachine
Gold Member
514
8

Homework Statement



Build a notation for the set: ##\{ ... , -8 , -3 , 2 , 7 , 12 , 17 ,...\}##

Homework Equations



##2+5(0) = 2##
##2+5(1) = 7##
##2+5(-1) = -3##

etc...

The Attempt at a Solution



##\{ \ 2+5y \ | \ y \in \mathbb{Z} \ \}##

Take note that you could replace ##2## by any elements of the set and it would still work.

any thoughts appreciated!

thank you!
 
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  • #2
reenmachine said:

Homework Statement



Build a notation for the set: ##\{ ... , -8 , -3 , 2 , 7 , 12 , 17 ,...\}##

Homework Equations



##2+5(0) = 2##
##2+5(1) = 7##
##2+5(-1) = -3##

etc...

The Attempt at a Solution



##\{ \ 2+5y \ | \ y \in \mathbb{Z} \ \}##

Take note that you could replace ##2## by any elements of the set and it would still work.

any thoughts appreciated!

thank you!

Looks fine... Do you have a question?
 
  • #3
No , just wanted to be sure it was correct.I'm slowly getting better at those.

Is that forbidden in this section? If so , I was unaware of it.

thank you!
 
  • #4
reenmachine said:
No , just wanted to be sure it was correct.I'm slowly getting better at those.

Is that forbidden in this section? If so , I was unaware of it.

thank you!
No, it's OK to get confirmation that you're on the right track.
 

FAQ: How Do You Express a Sequence Using Set Builder Notation?

1. What is set notation?

Set notation is a mathematical language used to represent and describe sets, which are collections of elements or objects. It uses symbols and mathematical operators to show the relationship between sets and their elements.

2. What is the difference between a set and a subset?

A set is a collection of elements, while a subset is a smaller set that is contained within a larger set. In other words, all elements of a subset are also elements of the larger set, but the larger set may have additional elements that are not in the subset.

3. How do you determine if two sets are equal?

Two sets are equal if they contain the same elements. This means that every element in one set is also in the other set, and vice versa. The order of elements does not matter in set equality.

4. What is the intersection of two sets?

The intersection of two sets is the set of elements that are common to both sets. This can be represented using the symbol ∩ and is read as "intersect." If the sets have no elements in common, then the intersection is an empty set.

5. How is set theory used in other fields of science?

Set theory has applications in various fields of science, including computer science, physics, and biology. It provides a foundation for understanding mathematical concepts and can be used to model and analyze real-world problems. For example, in biology, set theory can be used to classify and organize different species based on their characteristics.

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