# Math Confusion

Discussion in 'Odds & Ends' started by Talker, May 30, 2013.

1. ### TalkerHall of Fame

Joined:
Oct 4, 2007
Messages:
3,534
1) X = .99999...
2) 10X = 9.99999...

Subtract 1) from 2)

9X = 9 and X =1. So .9999.... = 1 and all is good.

1) Q = 1 + 2 + 4 + 8.........

2) Q = 1 + 2(1 + 2 + 4 + 8.........) Group terms

3) Q = 1 + 2Q Substitute 1) in 2)

Solve for Q:
4) Q = -1 and then -1 = Q = 1 + 2 + 4 + 8.........

How can -1 = 1 + 2 + 4 + 8......... ????

2. ### r2473G.O.A.T.

Joined:
Aug 14, 2006
Messages:
12,528
I've never really understood a person's Q score is calculated either.

3. ### sureshsBionic Poster

Joined:
Oct 1, 2005
Messages:
45,414
Because an infinite geometric series like Q does not converge unless the absolute value of the common ratio is less than 1. So Q does not exist in the mathematical sense, and its value is infinity.

4. ### LeeDBionic Poster

Joined:
Dec 28, 2008
Messages:
45,036
Location:
East side of San Francisco Bay
Because there is little value in math, translated to real life, unless you plan to be an accountant.

5. ### TalkerHall of Fame

Joined:
Oct 4, 2007
Messages:
3,534

You ruined all the fun.

Not rigorous way. If
1) Q = infinity
2) Q + 1 = infinity
Subtract 1) from 2) then

1 = 0

Q (infinity) is not a specific number like 400 for example or like you say does not converge to a specific number.

6. ### TalkerHall of Fame

Joined:
Oct 4, 2007
Messages:
3,534

As long as my bank account is positive I'm happy.

7. ### TalkerHall of Fame

Joined:
Oct 4, 2007
Messages:
3,534
People with low Q scores can't figure out their Q score.

8. ### krzProfessional

Joined:
May 23, 2007
Messages:
887
Location:
Concrete Jungle Where Dreams are Made

9. ### LeeDBionic Poster

Joined:
Dec 28, 2008
Messages:
45,036
Location:
East side of San Francisco Bay
Besides, the banks do it for you, and figure in their percentage while doing so....

10. ### ClaudiusProfessional

Joined:
Jun 4, 2009
Messages:
1,031
Most of use won't use calculus in our daily jobs, but then again do we really use anything we learned in grade school/college?

11. ### Steady EddyHall of Fame

Joined:
Jul 19, 2007
Messages:
3,280
Location:
Arizona
Maybe you don't use math in the way you do it on a math test? But having an understanding of math seems to matter. I read of a study that showed that people who could understand ideas like compound interest retired with much more \$\$ than did people who were ignorant of them.

12. ### r2473G.O.A.T.

Joined:
Aug 14, 2006
Messages:
12,528
Accounting has nothing to do with math.

13. ### The MeatHall of Fame

Joined:
Aug 9, 2012
Messages:
1,996
You pretty much only use Calculus when looking at graphs and want to figure out the amount of something under the curve or above the curve. After 3 years of undergrad research in Chemistry I can honestly say I've used Calculus a handful of times for my research papers. It's kind of a sad thing to admit......

14. ### GregNNew User

Joined:
Jan 11, 2005
Messages:
42
Talker, there is some real confusion with what you have 'assumed' not with maths as such. I would assume some lecturer has given these to you as a teaser, and its worked

15. ### Steady EddyHall of Fame

Joined:
Jul 19, 2007
Messages:
3,280
Location:
Arizona
What's wrong with the following?
Let "L" be the largest real number.
then surely 1) L >= 1
Since no real number can be larger than L, L >= L^2
Divide each side by L, and 2) 1 >= L
Combining 1) and 2)...1>= L >= 1,
so L must = 1

The largest real number is 1.

What's going on here?

16. ### sureshsBionic Poster

Joined:
Oct 1, 2005
Messages:
45,414
It has more to do with philosophy

17. ### sureshsBionic Poster

Joined:
Oct 1, 2005
Messages:
45,414
Eddy is back! Need to read his post and try to understand it.

18. ### r2473G.O.A.T.

Joined:
Aug 14, 2006
Messages:
12,528
Math and philosophy can be closely related.

19. ### Steady EddyHall of Fame

Joined:
Jul 19, 2007
Messages:
3,280
Location:
Arizona
I think so. Plato's academy didn't want those ignorant of geometry. Descartes, Leibniz, and Bertrand Russell are famous for contributions to mathematics and philosophy.

20. ### Baseline WinnerNew User

Joined:
Aug 18, 2012
Messages:
14
thats like saying infinite/infinite=one which is not always true.

21. ### Baseline WinnerNew User

Joined:
Aug 18, 2012
Messages:
14
I mean infinity...I can't spell

22. ### Steady EddyHall of Fame

Joined:
Jul 19, 2007
Messages:
3,280
Location:
Arizona
I think it is more like saying that 1 is the largest number, which is not true. It's clear the conclusion is wrong, but all the ideas leading up to that conclusion seem true. So, is logic unreliable?

23. ### Baseline WinnerNew User

Joined:
Aug 18, 2012
Messages:
14
What's wrong with this is the step where you have L>=L^2

You cannot both say that L=L^2 and L^2/L=L simply because if L is the largest real number L^2 (which we should then treat as infinity^2)=L so therefore this step should read that L>=L

24. ### Steady EddyHall of Fame

Joined:
Jul 19, 2007
Messages:
3,280
Location:
Arizona
First, I just want to be sure that there is no misunderstanding about ">=", which is "greater than or equal to", on this keyboard I cannot do the conventional symbol.

If I postulate a "largest real number", then it must have the property of being greater than its own square. Mathematicians think such an assumption is nonsense. But in philosophy, this kind of assumption is made in the ontological argument for god. I'm surprised philosophers don't dismiss it as well.

i.e. the ontological argument goes something like this. Imagine a most perfect being. Does this being exist? Yes, it must have the attribute of existence, otherwise we've not imagine the most perfect being. Hence, god exists.

p.s. Seems the arguments flaw is the assumption that a largest real number exists. Because such a number would have to be bigger than it's own square.

25. ### sureshsBionic Poster

Joined:
Oct 1, 2005
Messages:
45,414
There is no largest real number, because if L is the largest, L + 0.00000000001 is larger.

26. ### sureshsBionic Poster

Joined:
Oct 1, 2005
Messages:
45,414
They were one and the same in ancient times

27. ### CindysphinxG.O.A.T.

Joined:
Aug 31, 2006
Messages:
15,485
What's wrong?

It's math, that's what's wrong.

28. ### KineticChainHall of Fame

Joined:
Feb 26, 2012
Messages:
2,055
The technological world we thrive in today is thanks to the scientists and engineers who use math everyday

29. ### sureshsBionic Poster

Joined:
Oct 1, 2005
Messages:
45,414
LeeD doesn't care about technology. He likes to play sports outdoors and be One with Nature.

30. ### Steady EddyHall of Fame

Joined:
Jul 19, 2007
Messages:
3,280
Location:
Arizona
Yes, it takes for granted that L exists, just like the other argument assumed that 1 + 2 + 4 + 8...sums to a finite number.

Very true!

31. ### sureshsBionic Poster

Joined:
Oct 1, 2005
Messages:
45,414
Eddy, I just realized that there seems to be no direct way to generate the next prime number, given the previous one, except through various "sieve" schemes which actually just list possible candidates and eliminate the composite ones. In other words, given 7, there seems to be no direct way to find that 11 is the next prime number.

Has it been proven to be impossible? Not easy to find the answer from Google. Such a simple problem and no known solution!

32. ### Steady EddyHall of Fame

Joined:
Jul 19, 2007
Messages:
3,280
Location:
Arizona
This was discussed in "An Excursion Through Number Theory". We can't get a formula to generate primes because they're the numbers that haven't fit into any pattern yet. Something like that. I don't know if it has been proven. I'm at work now, but I'll look at that book when I get home. It's an inexpensive Dover book. I think you'd like it.

33. ### sureshsBionic Poster

Joined:
Oct 1, 2005
Messages:
45,414
These days I limit myself only to material which helps me teach my son. I will be free in a year or so once he is in college. Let me know if there is a proof that it cannot be done.

34. ### Steady EddyHall of Fame

Joined:
Jul 19, 2007
Messages:
3,280
Location:
Arizona
There is a proof that it cannot be done. On page 38 it says, "...they produce values of Y divisible by p, contradicting the hypothesis. Hence, no such prime producing polynomial exists.

35. ### ClaudiusProfessional

Joined:
Jun 4, 2009
Messages:
1,031
Here's a mindblowing fact.

There are infinitely many natural numbers, and infinitely many real numbers, right?

Well it turns out that the infinity of the real numbers is larger than the infinity of the natural numbers! To be mathematically precise, what this means is that there is no function from N --> R that is bijective. In other words, no one-to-one correspondence.

But get this. It just so happens that there as many rational numbers as natural numbers, and in fact, just as many integers as natural numbers!

In mathematics, we call this the cardinality of a set. For finite sets, the cardinality is simply the number of elements but for infinite sets it gets more interesting, and what cantor showed is that |N| < |R|.

It has long been conjectured that there is no set S, such that |N| < |S| < |R|. This was known as the continuum hypothesis. However, it won't ever be settled. Kurt Godel and Paul Cohen proved that the continuum hypothesis cannot be proven from the axioms of modern mathematics.

36. ### sureshsBionic Poster

Joined:
Oct 1, 2005
Messages:
45,414
And Cantor's diagonalization proof is ridiculously simple! I was quite surprised by how easy it is.

Do you know about infinities higher than R? I think there is one for the number of curves in 2D space? Probably 2 more infinities higher than R?

37. ### ClaudiusProfessional

Joined:
Jun 4, 2009
Messages:
1,031
There are infinitely many infinities higher than R. Take any set S. The set of all subsets of S is known as the power set of S (denoted P(S)), and it will always be the case that |S| < |P(S)|. For finite sets, this is obvious, since if S has n elements P(S) will have 2^n elements, but this extends to infinite sets as well. If interested, here's the proof.

Proof: It suffices to show that no function f: S --> P(S) can be surjective. Let A be the set of all elements x in S such that x is not in f(x). Then if x is in A, x is not in f(x), and so f(x) \= A. If x is not in A, then x is in f(x) \= A. Therefore, no element can get mapped to A, so f is not surjective.

Last edited: Jun 4, 2013
38. ### sureshsBionic Poster

Joined:
Oct 1, 2005
Messages:
45,414
What about the number of points in a plane? Is that infinity the same as the infinity of R because (x,y) both come from R?

What about the infinity of curves you can draw in a plane? Is it the same one as R?

39. ### ClaudiusProfessional

Joined:
Jun 4, 2009
Messages:
1,031

The set of points in the plane will have the same cardinality as R, same with the set of curves.

40. ### sureshsBionic Poster

Joined:
Oct 1, 2005
Messages:
45,414
But aren't curves like subsets of the points? Then their number should be that of the power set.

Joined:
Mar 11, 2011
Messages:
1,147
If your ... term is unlimited, Q = infinite and everything after that are completely meaning less.

If not, then you can't go from 1 to 2.

Joined:
Mar 11, 2011
Messages:
1,147
Logic is fine, the way you define and think/treat infinite is not.

You should not try to mix infinite and real number.

43. ### ClaudiusProfessional

Joined:
Jun 4, 2009
Messages:
1,031
You can think of a curve as a subset of the plane, but not all subsets of the plane is a curve. I admit, I can't quite prove the number of curves is |R|, but I'm rather certain of it.

44. ### r2473G.O.A.T.

Joined:
Aug 14, 2006
Messages:
12,528
Just as I can't prove that a large number of snakes on a plane = academy award, but I'm rather certain of it.