Question for the Math Gurus

[Crimson Wife]

DD is doing a section in Singapore Discovering Math 7B on set notation and she wants to know what the point of it is. I vaguely remember covering all these things (subsets, complements, etc.) but for the life of me cannot recall any practical application of it. Can anybody help?

[MyThreeSons]

I'll be interested to see what others have to say.

 

As with many other things, set notation is a tool. As one progresses in higher math, set notation is used to succinctly identify the limitations of a function, for instance. The logic and reasoning that are developed as one learns the fundamentals of set notation are also invaluable building blocks.

[dbmamaz]

yeah, i think set notation is mostly used in higher math. the first time we came upon it, in life of fred when dh was in 8th (and tried again in 9th) he totally flipped out about it and wanted to know what it had to do with math. by the time we got back to it (summer after 9th?) in singapore (we were using NSM) he seemed to just accept it.

[Dana]

It's also often seen in statistics courses.

Discrete math does a lot with sets.

[Iskra]

Set theory can be valuable in database design from what I remember.

It is sort of the "philosophy of mathematics" if you will. It is valuable to students of higher math if they want to study how we define just about anything in math. Any math object can be defined using set and group theory.

 

Here's the wikipedia article:

http://en.wikipedia.org/wiki/Set_theory

[Jane in NC]

Personally I think set notation is useful for categorizing. Here is an example that should give your daughter something to consider.

Example 27 There are 200 individuals with a skin disorder, 120 had been exposed to the chemical C₁, 50 to chemical C₂, and 30 to both the chemicals C₁ and C₂. Find the number of individuals exposed to

(i) Chemical C₁ but not chemical C₂ (ii) Chemical C₂ but not chemical C₁

(iii) Chemical C₁ or chemical C₂

 

Solution Let U denote the universal set consisting of individuals suffering from the skin disorder, A denote the set of individuals exposed to the chemical C₁ and B denote the set of individuals exposed to the chemical C₂.

Here n (U) = 200, n ( A ) = 120, n ( B ) = 50 and n ( A ∩ B ) = 30

(i) From the Venn diagram given in Fig 1.13, we have

A = ( A – B ) ∪ ( A ∩ B ).

n (A) = n( A – B ) + n( A ∩ B ) (Since A – B and A ∩ B are disjoint.)

or n ( A – B ) = n ( A ) – n ( A ∩ B ) = 120 –30 = 90

Hence, the number of individuals exposed to chemical C₁ but not to chemical C₂ is 90.

(ii) From the Fig 1.13, we have

B = ( B – A) ∪ ( A ∩ B )

and so, n (B ) = n (B – A) + n ( A ∩ B )

(Since B – A and A ∩ B are disjoint.)

or n ( B – A ) = n ( B ) – n ( A ∩ B )

= 50 – 30 = 20

Thus, the number of individuals exposed to chemical C₂ and not to chemical C₁ is 20.

(iii) The number of individuals exposed either to chemical C₁ or to chemical C₂, i.e.,

n ( A ∪ B ) = n ( A ) + n ( B ) – n ( A ∩ B )

= 120 + 50 – 30 = 140.

 

More here.

[Crimson Wife]

Set theory can be valuable in database design from what I remember.

 

 

 

That is useful information as my DD is very interested in computer programming. Thanks!

[Jane in NC]

A simple example of why understanding sets and the words "and"/"or": The I-9 employment form requires a job applicant to prove citizenship by submitting one document from column A or one document from group B and a second document from group C, I hire teenagers for a summer program and I am amazed at how many do not know the difference between "or" and "and".

[Laura in CA]

A simple example of why understanding sets and the words "and"/"or": The I-9 employment form requires a job applicant to prove citizenship by submitting one document from column A or one document from group B and a second document from group C, I hire teenagers for a summer program and I am amazed at how many do not know the difference between "or" and "and".

 

My son had to do this, and I remember scratching my head at first wondering if it was (A or B) and C, or A or (B and C) ... I don't think it was obvious! (not defending teenagers ... : )

[Laura in CA]

Haha, doing this on my phone made " B ) " into the sunglasses icon. Can't edit & am rushing off to dance class, but it should be obvious ... or at least give someone a good laugh ... : )

[flyingiguana]

A simple example of why understanding sets and the words "and"/"or": The I-9 employment form requires a job applicant to prove citizenship by submitting one document from column A or one document from group B and a second document from group C, I hire teenagers for a summer program and I am amazed at how many do not know the difference between "or" and "and".

 

I'm never sure of the answer to this on govt documents because I'm never sure if the person WRITING the document knew the difference between 'or' and 'and'.

[letsplaymath]

Set notation is used when you want to talk precisely about how things are defined and how they are related. Language is inherently imprecise, which can lead to some fun confusion (like these double-meaning headlines). But in math, we want to be able to communicate very precisely and to make sure that people understand exactly what we mean. Set notation lets us do that.

 

Even simple words like "or" have multiple meanings in language. In math and computer science, however, we have to be specific what type of "or" we are talking about: might both items be true? or do we mean it exclusively, one or the other but never both?