you should really make it clear that A union B =/= Comp(A) union Comp(B), the correct equation for De Morgan's Law is Comp(A union B) = Comp(A) intersection Comp(B). You have to negate the left side and in your video I think you got confused when you thought your underline for De Morgan's law was the bar indicating the complement
@mosow09 It highly depends on what type of set theory you are using. For general set theory (the elementary kind) I would recommend really starting with things such as wikipedia then looking at problems over google (papers are great resources to look up results :D). Set theory has a lot of very powerful results that affect all the formal sciences greatly. :) A good place to start is with any online book that covers elementary set theory.
The "set subtraction" thing described here afaik is usually called "symmetric difference", and the operation usually denoted by A - B or A \ B is the "relative compliment" meaning
lambda a, b: [x for x in a if not x in b]
(looks like python is the only language that can do this whose characters aren't blocked by youtube ^^)
Math makes my brain hurt, but this was significantly more enjoyable than any "math" class I've ever had.
I got the rest of it, but I'm a little confused about how the answer for that set subtraction you did was empty set and not {2} but I probably missed something.
the reason it is empty set is because, we are subtracting from set A. Set subtraction is bizarre like that. If A doesn't have it then you can't subtract it.
When using sets in alegebra do you need both of the notations? Set builder notation and the Roster notation? Can just the roster notation just be used alone?
For example. The x=51, so cant that be writen as x={51} or x={-5,-4,-3,-2,-1,0,1,2,3,4,.....51}
Cant any varible represent an element or some kind of set? After all its a viariable and it has to be something like an integer, rational, irational number, right?
{51} != 51. One is a set containing 51, and the other is just an integer of 51.
Yes a variable can be represented as some set of values. Typical use is considered an array of elements in a set where you can iterate over some a_i contained in S. Sets can contain anything you like from symbols to algebraic expressions to variables and even operators.
For the question about the 1st one. You can express the solutions as a set.
Can I write the Varibale in this algebraic equation as a set or an element of a set?
Problem: Jeanne has $17 in her piggy bank. How much money does she need to buy a game that costs $68?
Solution: Let x represent the amount of money Jeanne needs. Then the following equation can represent this problem: 17 + x = 68 We can subtract 17 from both sides of the equation to find the value of x. 68 - 17 = x
Answer: x = 51, so Jeanne needs $51 to buy the game.
yes, you can. Typically when something is mathematically defined it usually is a set (an ordered pair within a set).
Set Theory is nice since it is typically the foundation of mathematical definitions. For instead if you had variables x and y. If you had a Cartesian plane, the plane is made out of ordered pairs (x,y) which are contained in some set {x,y}. Functions in general are something called a bijection from x onto y f:x->y.
So the undefined variable is one of the those elements in that set? For example in physics you have M=MC squared, that famous Einstien equation. I know they are constants but since they are letters they can be shown as either integers, counting numbers or whole numbers, ect.
M = MC squared are all reals. Those are not countable since reals are not countable. One could use a set to contain the variables though :) within a given precision one could assign them (computer programs do something like this). S = {M,C} then if you say were doing the computation you could just store M and C within this set to save you computations later on :). You can literally use a set to be a collection of any set of objects as long as they are countable unless you want infinite sets.
If you wanted to denote this as a set relation you could easily use a function (like how the formula is given in) unless you wanted to represent variables and results. I hope that answers your question :).
yes thanks. That answerd it. So reals are the entire set of irrational numbers and rational numbers? Physics and science use big numbers and put exponents on them to denote how big the numbers are. So something like planks constant would be a Real number?
yes. Thats the reals. It is an infinite set (so it cannot be counted).
Anything that is burden to error will be a real number (anything you would measure is real numbers since there is no such thing as an exact measure in empirical sciences). :)
I hope I can understand it. I suck at math :P
kylaawright 6 months ago
you should really make it clear that A union B =/= Comp(A) union Comp(B), the correct equation for De Morgan's Law is Comp(A union B) = Comp(A) intersection Comp(B). You have to negate the left side and in your video I think you got confused when you thought your underline for De Morgan's law was the bar indicating the complement
Dinunzilicious 9 months ago
@Dinunzilicious yes you are correct. My apologies.
Entertainmentwf 9 months ago
Great vid thanks alot, do you know of any websites where I can further learn about sets for like test prep??
mosow09 11 months ago
@mosow09 It highly depends on what type of set theory you are using. For general set theory (the elementary kind) I would recommend really starting with things such as wikipedia then looking at problems over google (papers are great resources to look up results :D). Set theory has a lot of very powerful results that affect all the formal sciences greatly. :) A good place to start is with any online book that covers elementary set theory.
Entertainmentwf 11 months ago
Good Explanation, found it easy to understand
nickcooper28 1 year ago
great vid!!!
makado1980 1 year ago
Why is that none of your other videos focus on math?
ambigera 1 year ago
@ambigera I plan to do many more. I just tend to go on tangents with my theoretical stuff and my game development stuff.
Entertainmentwf 1 year ago
cant relli hea him
sexy19081995 1 year ago
The "set subtraction" thing described here afaik is usually called "symmetric difference", and the operation usually denoted by A - B or A \ B is the "relative compliment" meaning
lambda a, b: [x for x in a if not x in b]
(looks like python is the only language that can do this whose characters aren't blocked by youtube ^^)
Ormaaj 2 years ago
lol, pretty much. I just stuck with the general definitions for ease of complexity..
Entertainmentwf 2 years ago
You freak me out with your left handed writing. Great and helpful tutoral. helps alot.
RGB271979 2 years ago
anytime :D. Ya I'm a minority LOL. It even freaks me out LOL.
Entertainmentwf 2 years ago
anytime :). Ever have any questions feel free to ask :D!
Entertainmentwf 2 years ago
Haha... multiple MSN chimes.
Math makes my brain hurt, but this was significantly more enjoyable than any "math" class I've ever had.
I got the rest of it, but I'm a little confused about how the answer for that set subtraction you did was empty set and not {2} but I probably missed something.
Nice whiteboard crisis aversion.
And another great vid. =D
HyperMushrooms 2 years ago
the reason it is empty set is because, we are subtracting from set A. Set subtraction is bizarre like that. If A doesn't have it then you can't subtract it.
Entertainmentwf 2 years ago
So if it was B / A the result would be {2}, wouldn't it?
Thank you! :)
slvadi 2 years ago
yes :).
Entertainmentwf 2 years ago
When using sets in alegebra do you need both of the notations? Set builder notation and the Roster notation? Can just the roster notation just be used alone?
199tinkerbell 2 years ago
you can use either. Builder notation works well with definitions. Typically when working with sets alone roster is good but, either is wonderful.
Entertainmentwf 2 years ago
For example. The x=51, so cant that be writen as x={51} or x={-5,-4,-3,-2,-1,0,1,2,3,4,.....51}
Cant any varible represent an element or some kind of set? After all its a viariable and it has to be something like an integer, rational, irational number, right?
199tinkerbell 2 years ago
Okay to answer your questions :)
{51} != 51. One is a set containing 51, and the other is just an integer of 51.
Yes a variable can be represented as some set of values. Typical use is considered an array of elements in a set where you can iterate over some a_i contained in S. Sets can contain anything you like from symbols to algebraic expressions to variables and even operators.
For the question about the 1st one. You can express the solutions as a set.
Entertainmentwf 2 years ago
Can I write the Varibale in this algebraic equation as a set or an element of a set?
Problem: Jeanne has $17 in her piggy bank. How much money does she need to buy a game that costs $68?
Solution: Let x represent the amount of money Jeanne needs. Then the following equation can represent this problem: 17 + x = 68 We can subtract 17 from both sides of the equation to find the value of x. 68 - 17 = x
Answer: x = 51, so Jeanne needs $51 to buy the game.
199tinkerbell 2 years ago
yes, you can. Typically when something is mathematically defined it usually is a set (an ordered pair within a set).
Set Theory is nice since it is typically the foundation of mathematical definitions. For instead if you had variables x and y. If you had a Cartesian plane, the plane is made out of ordered pairs (x,y) which are contained in some set {x,y}. Functions in general are something called a bijection from x onto y f:x->y.
Entertainmentwf 2 years ago
So the undefined variable is one of the those elements in that set? For example in physics you have M=MC squared, that famous Einstien equation. I know they are constants but since they are letters they can be shown as either integers, counting numbers or whole numbers, ect.
MsBigdave12 2 years ago
M = MC squared are all reals. Those are not countable since reals are not countable. One could use a set to contain the variables though :) within a given precision one could assign them (computer programs do something like this). S = {M,C} then if you say were doing the computation you could just store M and C within this set to save you computations later on :). You can literally use a set to be a collection of any set of objects as long as they are countable unless you want infinite sets.
Entertainmentwf 2 years ago
If you wanted to denote this as a set relation you could easily use a function (like how the formula is given in) unless you wanted to represent variables and results. I hope that answers your question :).
Entertainmentwf 2 years ago
yes thanks. That answerd it. So reals are the entire set of irrational numbers and rational numbers? Physics and science use big numbers and put exponents on them to denote how big the numbers are. So something like planks constant would be a Real number?
MsBigdave12 2 years ago
yes. Thats the reals. It is an infinite set (so it cannot be counted).
Anything that is burden to error will be a real number (anything you would measure is real numbers since there is no such thing as an exact measure in empirical sciences). :)
Entertainmentwf 2 years ago
Define what you mean by an undefined variable is one of the elements in that set?
Entertainmentwf 2 years ago