This Blog exists for the collective benefit of all algebra students. While the posts are specific to Mr. Chamberlain's class, any and all "algebra-ticians" are welcome. The more specific your question (including your own attempts to answer it) the better.
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Friday, November 12, 2010
hw #3-6 FUN with SETS... Unions, Intersections, and more!
hw #3-6
pg 218-219 #10-21 ALL
#23-29 Odd
pg 220 #49-63 ALL
You should be looking at pg 223-226 #1-61 ALL in preparation for the UNIT TEST on Thursday...
Hi mr. c! Im confused about problem #27. The book only gives you an example of if its an and inequality, not an or inequality like prob 27. How would you write it if its a union?
oops wait i think i fiqured it out, but now im having trouble with number 29. I think this one is a union, but i dont understand how to write it. would you just write set builder notation for each inequality serparately?
Good question, Julia. We touched very briefly at the end of the period on the comparison between "AND and OR inequalities" vs. "Intersections and Unions."
Let's take a random AND INEQUALITY such as:
33 AND x<=9 (do you agree?)
It could also be written in interval notation:
(3,9]
Now, if we took the UNION of x>3 and x<=9, we would include ALL REAL NUMBERS, since x>3 goes all the way to ∞ and x<=9 goes all the way to -∞. If we took the INTERSECTION of x>3 and x<=9, then we accept as solutions ONLY the numbers that are solutions for both inequalities at the same time... in other words only the real numbers that are > 3 and <=9 satisfy both inequalities simultaneously, SO THEREFORE, an AND INEQUALITY is synonymous with an INTERSECTION.
I'm hoping you could fashion a similar argument to prove the synonymy between an OR INEQUALITY and a UNION. Can you?
Yeah, I'd like to see someone explain that myself... maybe I can even find some room for some last-minute extra-credit now that the first marking period is closed?!
Julia (or anyone)... are you OK with set notation and inequalities, or is it still a little muddy? If muddy, can you articulate a question?
Thanx for the help on OR inequalities. I think I get it now. Can we still go over it in class more on Tues? That would help me more, the book doesn't really give a good explanation. I am ok w/ set builder notation and inequalities.
Yup... Tuesday is half review; half new unit... so come prepared with questions... you should be looking at (and maybe doing some) of the chapter review problems on pgs 222-227.
OK, thanks for trying AND JUST AS IMPORTANTLY THANKS FOR LETTING ME KNOW. We'll just have to review it in class. If you have a question on it, so do several others!
If anyone thinks they can describe it better, now would be a great time to buzz in. I'll be out for the rest of the evening.
Hi mr. c! Im confused about problem #27. The book only gives you an example of if its an and inequality, not an or inequality like prob 27. How would you write it if its a union?
ReplyDeleteoops wait i think i fiqured it out, but now im having trouble with number 29. I think this one is a union, but i dont understand how to write it. would you just write set builder notation for each inequality serparately?
ReplyDeleteGood question, Julia. We touched very briefly at the end of the period on the comparison between "AND and OR inequalities" vs. "Intersections and Unions."
ReplyDeleteLet's take a random AND INEQUALITY such as:
33 AND x<=9 (do you agree?)
It could also be written in interval notation:
(3,9]
Now, if we took the UNION of x>3 and x<=9, we would include ALL REAL NUMBERS, since x>3 goes all the way to ∞ and x<=9 goes all the way to -∞. If we took the INTERSECTION of x>3 and x<=9, then we accept as solutions ONLY the numbers that are solutions for both inequalities at the same time... in other words only the real numbers that are > 3 and <=9 satisfy both inequalities simultaneously, SO THEREFORE, an AND INEQUALITY is synonymous with an INTERSECTION.
I'm hoping you could fashion a similar argument to prove the synonymy between an OR INEQUALITY and a UNION. Can you?
Did this help? Let me know.
Mr. C.
I'm still confused with inequalities/equations with no solution.. Could someone explain that?
ReplyDeleteYeah, I'd like to see someone explain that myself... maybe I can even find some room for some last-minute extra-credit now that the first marking period is closed?!
ReplyDeleteJulia (or anyone)... are you OK with set notation and inequalities, or is it still a little muddy? If muddy, can you articulate a question?
Thanx for the help on OR inequalities. I think I get it now. Can we still go over it in class more on Tues? That would help me more, the book doesn't really give a good explanation. I am ok w/ set builder notation and inequalities.
ReplyDeleteYup... Tuesday is half review; half new unit... so come prepared with questions... you should be looking at (and maybe doing some) of the chapter review problems on pgs 222-227.
ReplyDeleteHmmm... I guess I never answered the question... (that's what can happen when you get so excited discussing the underlying math!)
ReplyDeleteTo write an AND inequality like:
x>3 and x<=9 in set notation, you would write:
x>3 intersects (i.e. upside-down U) x<=9
To write aOR inequality like:
x<3 OR x>=9 you would write:
x<3 U x>=9
Does THAT answer the question?!
Mr. C.
Mr. C...I read your convo with Julia...but I am still not sure. I have the same question.
ReplyDeleteOK, thanks for trying AND JUST AS IMPORTANTLY THANKS FOR LETTING ME KNOW. We'll just have to review it in class. If you have a question on it, so do several others!
ReplyDeleteIf anyone thinks they can describe it better, now would be a great time to buzz in. I'll be out for the rest of the evening.