Transcendental property of equality: if a=b and b=c, then a=c. That .999…=x was given. From that I proved that x=1. Thus, since .999…=x=1, .999…=1.
Can anyone here explain how the delta-epsilon definition of a limit applies when the limit is infinity? I tried doing it, but everything went kablooie.
Okay, I get that…I wasn’t thinking. I am, however, still confused on this:
I only see x on the left side?
Oh, and delta-epsilon definition - is that:
lim f(x) = L
x > c
= goes to
alright, lambda calculus and combinatory logic. anyone else kinda drools every time they realise once again how exactly the Y combinator works?
Right side is 9.999…
X=0.999…
9.999…-X=9.999…-0.999…=9.
I admit that it’s not at all obvious that that’s allowed.
And for the limit, thanks, but that’s not exactly what I was looking for.
I know. 
I was trying to confirm that what I posted is the delta-epsilon “version” of the limit.
The delta epsilon definition says that “the limit as x approaches c of f(x)=L” means that for any epsilon (e) > 0, there is a delta (d) > 0 such that if 0<|x-c|<d, then |f(x)-L| < e.
I need help! 
Probability
-
You have a deck of cards (52 cards), and pick three.
What’s the probability to pick 3 different colors? -
A family has 4 kids.
What’s the probability that there are 2 boys?
(By the way: P(boy) = 0.516), and P(girl) = 0.486)
I know the answeres, but not how to calculate it 
A straight deck of 52 cards is four sets of 13 cards each. You make a first pick at random, taking one card away from the set you picked a card from: (13 + 13 + 13 + 13) = 52
↓
(13 + 13 + 13 + 12) = 51. So now the chance that you get a different set is the sum of cards in the three remaining sets, over the sum of possible cards: (313)/51. This also changes the number of cards: (13 + 13 + 12 + 12) = 50. So for our last draw, the chances are: (213)/50. The total probability is: (313)(213)/(51*50).
Does that help?
Thanks Bruno, but it’s wrong 
In the book the solution is:
- 39.8 % chance to get three different colors.
- 37.4 % chance that there’s two boys in the family.
It was a good try.
Bruno’s answer was (313)(213)/(51*50) ant it’s 0.3976 which rounds to 39,8%, so it’s correct.
Probability of two boys is (4!/(2!2!))P(boy)^2P(girl)^2 (that’s because there will be two boys and two girls, hence P(boy)^2P(girl)^2, and there are 6 ways (4!/(2!2!)) that give 2 boys and 2 girls - for example the first two are boys, the second two are girls, or the first one is a boy, then 2 girls, then one boy etc.)
With your data P(boy)+P(girl)=1.002 which is not good, so I’ll assume P(boy)=0.514. Then P(2 boys) = 60.514^2*0.486^2 = 0.3744 = about 37.4%
Well then, it’s right! 
(313)(213)/(51*50) = 0.3976… = 39.8%.
Hahaha, I’m so stupid. Must have pressed something wrong on the calculator. 
And yes, P(boy) = 0.514, and not 0.516.
Thank you so much for the help Bruno and Fizyk 
WHAT!!! How do you pass Math I failed 3 years and counting…
WOW! A topic where you can get help with math? 
Oh wait, I think I already knew about this, but I probably dismissed it as nerdy.
any of you good with calculus? I’m gonna start asking questions in here. 
anti-derivatives, u-substitution, and 
I totally forgot what I was doing in math since I’ve had the last week off!
Ask away. I, at the least, can assist.
So I just saw the proof of Euler’s formula (e^(pi*i)+1=0). It’s beautiful. I almost drooled.
The proof of what? Ugh I can’t read this topic I actually get a hedache…
That e^(pi*i)+1=0, where e is Euler’s number, being the base of the natural log, approximately 2.718, pi is the ratio of a circle’s circumference to its diameter, approximately 3.14159, and i is the square root of -1, an imaginary number.
This, by the way, is exactly why we need proofs. No one would believe it otherwise.
Dude… you are aware that Led Zeppelin made intense use of yes, you guessed it Maths, in the process of composing their albums. Right?