Anyone here into math?

[Guest [ch...]]

5! = 5 * 4 * 3 * 2 * 1 = 120

5!! = 5 * 3 * 1 = 15

I've never seen that definition of "!!".

I would have said 5!! is 6689502913449127057588118054090372586752746333138029810295671352301633557244962989366874165271984981308157637893214090552534408589408121859898481114389650005964960521256960000000000000000000000000000

[Guest [ch...]]

Lfree, your Ativan math post is pretty funny

[Guest [ch...]]

Time for some math jokes...

 

Pi and -1 walk into a bar.

"I identify as rational" said Pi.

"You cannot be a fraction" said -1

"Oh, stop being so negative" said Pi.

 

An infinite number of mathematicians walk into a bar

"I'll have 1/2 a beer" the first said.

"I'll have 1/4 of a beer" the second said.

"I'll have 1/8 of a beer" the third said.

...

The bartender interrupts them and pours 1 beer and says "you guys should know your limits"

 

 

[Guest [ch...]]

[[Es...]]

I always liked math, but ended up working on programming projects where advanced knowledge of math wasn't required, so yes, I am in the same boat as far as the ability to solve problems.

 

count me in the sane boat lorazepam! pascal was the first language i was taught in comp. sci. in school. that was 1989. i loved pascal. pascal was never meant to be used commercially and its intended purpose was its use as an educational language to introduce data structures to students. but now kids get exposed to programming much earlier in life, so pascal has lost its relevance. my kids were taught blue java, i think, in school, when they were maybe 10! so they don't need to learn pascal. also many new, better languages have been developed in the interim.

 

yes, comp. sci. does not require much math knowledge. i agree with you. i have a friend who spent his life lecturing in various universities in india and US. he holds a double phd in comp. sci. and electrical engineering. when i was confused with cantor, a few days ago, i ran to him. he told me in no uncertain terms that he was not a phd in math and that he was as much a novice in number theory as i was. for comp. sci., he said, he needed mostly predicate calculus and not number theory.  it then took me a good number of days to understand these concepts on my own. and i have just scratched the surface!

 

I think I really first started with BASIC, as so many do. Then in high school we had courses in BASIC, Pascal and later Fortran, which I never used. Then going to college, the introductory course was Pascal, then C, then C++. Then I also learned COBOL as well, which actually ended up being very handy (knowing legacy and new languages was a big asset to my career for a long time). But I really liked when Borland created Delphi, and I remember working with Visual Basic and SQL Server, and playing around with Delphi and realizing how much more evolved and elegant programming platform was than either Microsoft Visual Basic of MS Visual C++ MFC and ATL. But companies used to stick with Microsoft because "no manager ever got fired for buying Microsoft". So anyway. I transitioned from Visual Basic to VB.Net, which really was a totally different language. Of course, I learned some html and vbscript and ASP and javascript on the way too. Then I had some interesting experiences, working on languages such as PowerBuilder and Visual FoxPro. PowerBuilder was unique and interesting, but I never liked Visual FoxPro much. Then, of course, the unavoidable MS Access and more .NET (VB.NET and ASP.NET). My .Net knowledge got really good in the 00's and had switched to working on C# around 2010. Also had a chance to work on Oracle DB with PL/SQL for a year or so. After that, it was back to ASP.NET, VB.NET and SQL Server again.

 

Honestly, I'll always love Pascal/Delphi. I know that Pascal has sort of been thought of as a university language and not meant for writing commercial code, Borland's Delphi had lots going for it, and a lot of Microsoft .Net programming technology was built by ex-Borland engineers (Anders Hejlsberg comes to mind). And it's amazing how much Oracle's PL/SQL borrows from Pascal in terms of creating units with interface and implementation section.

 

I actually thought that the whole Microsoft COM interface borrowed heavily from Pascal/Delphi, PowerBuilder.

 

Even though being a Visual Basic programmer in the 90's paid decent, it never ceases to amaze me how there were so much better rapid development languages available that companies were afraid to purchase. But then again, Microsoft was not going anywhere, so there was that safety.

 

I keep looking back at my career choices, and wonder what would have happened if I ditched Microsoft and just went to work on Oracle and PL/SQL. It would have been lot less stressful, as the platform doesn't change as much, and it would have given me more time for personal life aside from work, rather than learning every new Microsoft's iteration and permutation of everything.....

 

LRF, you are amazing You could as well be talking Chinese as far as I’m concerned...

[[Es...]]

Shouldn’t be looking at this thread... I will get a huge inferiority complex...

[[Lo...]]

Shouldn’t be looking at this thread... I will get a huge inferiority complex...

 

No, it's ok. Ever since this happened to me, all that stuff became very foggy. I can tell you what I worked on, but trying to work on any of that right now would be impossible. I think that's so frustrating about this condition. Panicked out of my mind while brain is not cooperating....

[[Lo...]]

5! = 5 * 4 * 3 * 2 * 1 = 120

5!! = 5 * 3 * 1 = 15

I've never seen that definition of "!!".

I would have said 5!! is

<pre>

66895029134491270575881180540903725867527463331380298102956713523016335572449629893668741

652719849813081576378932140905525344

08589408121859898481114389650005964960

521256960000000000000000000000000000

</pre>

 

Oh, I see where I went wrong:

 

5!! = (5!)!

    = (120)!

    = (5 * 4 * 3 * 2 * 1)!

    = (120)!

 

Ok,  things making sense again.

[[Lo...]]

Shouldn’t be looking at this thread... I will get a huge inferiority complex...

 

It's ok, Estee. None of this is as difficult as it actually seems. Most people have a potential to be really good at math or computer stuff. It's just that the subjects seem intimidating, but it's usually because they are culturally seen as intimidating. I had a very intimidating, difficult math teacher in 5th grade, and my math grade plummeted. As soon as I moved to another school and another part of town and got a more compassionate, patient teacher, my math grades were resurrected. I've seen math & science teachers that will instill unnecessary fear and anxiety into their students. I am not sure why some of them do that, but they clearly do. Comes back to egos, I guess. Or maybe they're just overworked, underpaid and burnt out, just like it happens to many in different professions. But, interestingly, our high school physics teacher was an Oxford educated woman with a master's degree, and she made everyone's life a horror story. She treated us as University Students, not high school kids. But her husband was a PhD, and she may have wanted to be the University Professor that she always wanted to be, but was unable for various reasons. I could imagine a marriage of two scientists/researchers being fiercely competitive.

 

[[Es...]]

LRF, all Universe can be explained by laws of mathematics, physics, chemistry etc. I’ve always been into literature. So many unnecessary words. I thought if I studied philosophy, logic and learnt about psychology. I would be so wise. But these are just theories of imperfect human minds.

 

Every philosopher was influenced by his upbringing, brain chemistry, life experience etc. The same goes for every psychologist. Freud was into coke. Nietzsche was into all kinds of mind-altering substances. Yeah, a literary genius. But what do his theories actually explain. Math isn’t influenced by anything. I was only into words. I was wrong. One of my fav philosophers, Blaise Pascal. Was actually first of all brilliant mathematician and physicist.

 

Maybe you’re right. Those things do seem intimidating. But to learn them requires time and effort. This is a potential which should be invested. I remember those IT guys coming to our room for an hour or so. To fix sth on our PCs. We just stared blankly. I was trying so hard to understand what they were doing. I don’t understand to this day.

[[Lo...]]

LRF, all Universe can be explained by laws of mathematics, physics, chemistry etc. I’ve always been into literature. So many unnecessary words. I thought if I studied philosophy, logic and learnt about psychology. I would be so wise. But these are just theories of imperfect human minds.

 

Every philosopher was influenced by his upbringing, brain chemistry, life experience etc. The same goes for every psychologist. Freud was into coke. Nietzsche was into all kinds of mind-altering substances. Yeah, a literary genius. But what do his theories actually explain. Math isn’t influenced by anything. I was only into words. I was wrong. One of my fav philosophers, Blaise Pascal. Was actually first of all brilliant mathematician and physicist.

 

Maybe you’re right. Those things do seem intimidating. But to learn them requires time and effort. This is a potential which should be invested. I remember those IT guys coming to our room for an hour or so. To fix sth on our PCs. We just stared blankly. I was trying so hard to understand what they were doing. I don’t understand to this day.

 

Exactly. Good points. One interesting thing about computer programming/software engineering is that the systems that these people work on are made for different industries, so usually a programmer working for a healthcare company has to know a lot about that business, too.  A programmer for an insurance company has to learn more than a thing or two about insurance business. Sometimes, programmers specialize and stay within the same domain for years (engineering, research, healthcare, accounting, government), but many times, over the course of the careers, they change the domain where they work, and even though their core knowledge is the same, they end up working in completely different businesses. This is what you'd call a secondary knowledge. And this is where it gets interesting is that sometimes a programmer/engineer/analyst gains so much knowledge about the industry they work in that they often end up being more valued for that secondary knowledge than the programming knowledge they possess, which may actually end up leading to a programmer being converted into an analyst, by the virtue of being given fewer programming projects and more tasks, strictly related to the business part of the place where they work. It's not good or bad. It just sometimes is.

[Guest [ou...]]

Threads are like the Hotel California. You can check out anytime you want like, but you can never leave.

 

Nice one and apparently true.

 

i read up real numbers and realized that my understanding of numbers is woefully inadequate.

 

Your words not mine. I think your problem is you 'see' Cantor everywhere.

 

any sum of rationals will generate only a countable number.

 

There is no such thing as a countable number; only countable SETS of numbers.

 

what you get by your formula is only a finite sequence of pi.

 

Only because you stop after finitely many number of steps.

 

irrationals have no algorithm (you cannot even write them).

 

WRONG. Here is an algorithm for computing the Nth digit of Pi.

Write them? You cannot even write 1/3 in decimal form. 0,333... is just 3 digits and 3 dots,

plus it's also an infinite sum 3/10+3/100+3/1000+...=1/3 which HAPPENS to be rational.

 

pi is the sum of numbers rational and irrational.

NO. Just rationals. I know this may seem paradoxical so let me explain.

IRrationals are NOT rationals but that is not their definition.

In fact, irrationals are defined USING rationals through Dedekind cuts,

not unlike rationals are defined using integer division.

[Guest [ou...]]

x + y^2  = 25

x = 5

 

y = sqrt(20)

 

 

Calculate the sum of numbers from 1 to 100: 5050

 

For the love of whatever God you may believe in, stop posting problems along with their solutions.

Either post easier ones or wait a bit. The whole point of this thread is to exercise our benzo-brains.

[Guest [ou...]]

Time for some math jokes...

 

http://upload.wikimedia.org/wikipedia/commons/e/e8/Pi-day-funny-math-be-rational-get-real.jpg

[Guest [ou...]]

Now time for some math before we move on to programming.

 

Problems:

 

1. Show that

a. the square of an odd number is of the form 8k+1

b. x^4+6x^2-7 is a multiple of 128 when x is odd

 

2. Solve y^2=x^2+3 when x,y are positive integers

 

3. Simplify X=√(2+√(2+√(2+...)))

 

4. Express f(x)=1+2x+3x^2+... in closed form when |x|<1

 

Solutions:

 

 

1. The product of 2 consecutive integers is even.

 

a. (2n+1)^2 = 4n^2 + 4n + 1 = 4*n(n+1) + 1 = 4*(2k) + 1 = 8k+1

b. x^4+6x^2-7 = (x^2)^2+6x^2-7 = (8k+1)^2+6(8k+1)-7 = 64k^2+64k = 64*k(k+1) = 64*(2n) = 128n

 

 

Problem 2.

 

y^2=x^2+3 <--> y^2-x^2=3 <--> (y-x)(y+x)=1*3 -->

y-x=1 and y+x=3  <-->  x=1 and y=2

 

 

Problem 3.

 

X=√(2+√(2+√(2+...)))=√(2+X) -->

X^2=2+X <--> X^2-X-2=0 <-->

X=2 or -1<0

 

 

Problem 4.

 

f(x)=1+2x+3x^2+...

xf(x)=0+x+2x^2+...

(1-x)f(x)=1+x+x^2+...

x(1-x)f(x)=0+x+x^2+...

(1-x)(1-x)f(x)=1

f(x)=1/(1-x)^2

[[Lo...]]

For the love of whatever God you may believe in, stop posting problems along with their solutions.

Either post easier ones or wait a bit. The whole point of this thread is to exercise our benzo-brains.

 

For the love of God, can't you be a little more civil? Why so harsh??

[Guest [ou...]]

For the love of whatever God you may believe in, stop posting problems along with their solutions.

Either post easier ones or wait a bit. The whole point of this thread is to exercise our benzo-brains.

 

For the love of God, can't you be a little more civil? Why so harsh??

 

Sorry. I didn't mean to be mean (no pun intended).

I'd been absent from my own thread for some time and was in a hurry to respond to everything.

[Guest [ou...]]

Let f(x)=e^x+x-2

 

Since f is increasing it has at most 1 root.

Since f(0)f(1)=(-1)(e-1)=1-e<0 f has exactly 1 root in (0,1).

 

Problem: Develop an algorithm that approximates that root given a tolerance "err".

 

Notes:

 

1. Answers may be given in Pascal or pseudocode as:

 

i loved pascal.

 

I also took a course in Pascal.

 

I'll always love Pascal/Delphi.

 

2. To chessplayer: In case you find this easy,

give the rest of the group a couple of days before posting your answer.

[Guest [Kp...]]

i read up real numbers and realized that my understanding of numbers is woefully inadequate.

 

Your words not mine. I think your problem is you 'see' Cantor everywhere.

 

that is true outis. but the next day i also said that though i read godel in college, i understood him deeply only now. so the next day i did get a grasp of reals. i still consider my knowledge inadequate because my last comment was that having scratched the surface of number theory, i was no longer interested in ploughing further.  i would not have participated in this thread after that point had you not made an untrue statement about irrationals. that i do not want to learn anything more about numbers does not mean i am unwilling to teach what i already know about numbers. 

 

it also does not mean that i cannot know more about real numbers than you do. remember, i studied godel in college and i had thought i understood it but i hadn't. i understood it thirty years later. that is a long time. it also means that understanding godel was not critical to my life. so it is ok if you don't understand two infinities because you can still do math and physics as long as you follow the rules (which you will if you have memorized them). understanding rules was never a rigorous prerequisite in science -- it is why computers can do math (computers follow a "consistent" logic. hawking speaks of "consistency" of physical theories in his essay on godel. godel proved that logic was "consistent and incomplete." godel also proved that you cannot prove the consistency of any logical system using its own logic, so godel proved the consistency of our logical system by using another logical system called "type." consistency means you cannot derive contradictions from the axioms of the language. if a computer follows consistency, it does not have to understand the meaning of the rules. just because hawking thinks he is writing for laymen, it does not mean laymen will understand him). and please do not take my comments otherwise because your confusion is very natural. you will recall that i had told you that cantor was persecuted by his influential peers for his two infinities proof. a similar thing is happening here although you are not persecuting me but only having difficulty understanding the concept and till now you haven't accepted that "you are having difficulty."

 

i have heard of dedekind cuts but i do not know what they are. yet i can say that your understanding that dedekind cuts can generate irrationals is wrong. like chessplayer, you are only misunderstanding sites and texts. i see cantor everywhere because cantor "exists" everywhere. you have to realize this if you truly want to "understand" cantor (which, to repeat, is optional if you just accept his theorem).

 

one algorithm for generating any rational number is writing it down. turing proved this and the proof is the meeting ground between turing and cantor. it is called the church-turing thesis.

 

church-turing thesis states that a function on the natural numbers is computable by a human being following an algorithm, ignoring resource limitations, if and only if it is computable by a turing machine.

 

so when you say that a function on the natural numbers using dedekind cuts can generate an irrational number, without resource limitations (to infinity), then you are saying that irrational numbers are turing computable. if irrational numbers are turing computable, then turing is wrong because turing said that some algorithms are not turing computable whereas you are saying all algorithms are turing computable. (rationals can be expressed as a fraction so they are "defined" as being turing compatible, so the irrationals are the only non rationals and together they constitute the set called real numbers).

 

 

 

[[Es...]]

Exactly. Good points. One interesting thing about computer programming/software engineering is that the systems that these people work on are made for different industries, so usually a programmer working for a healthcare company has to know a lot about that business, too.  A programmer for an insurance company has to learn more than a thing or two about insurance business. Sometimes, programmers specialize and stay within the same domain for years (engineering, research, healthcare, accounting, government), but many times, over the course of the careers, they change the domain where they work, and even though their core knowledge is the same, they end up working in completely different businesses. This is what you'd call a secondary knowledge. And this is where it gets interesting is that sometimes a programmer/engineer/analyst gains so much knowledge about the industry they work in that they often end up being more valued for that secondary knowledge than the programming knowledge they possess, which may actually end up leading to a programmer being converted into an analyst, by the virtue of being given fewer programming projects and more tasks, strictly related to the business part of the place where they work. It's not good or bad. It just sometimes is.

 

Yeah, LRF. Know many guys who’ve worked as IT programmers in the same field for decades. They are almost revered there. No one would ever imagine them leaving. They earn very good money. I don’t think their jobs are stressful. Some work real hard and cover for those who are just lazy. I’m talking about govt. institutions. Don’t really know how it looks in the private sector. Stayed there for a brief period of time and it was too much work and pressure. In spite of huge money. No reasonable HR policy. Treated ppl like objects to be used and discarded. Well, my country’s private sector is a particularly inhuman place. Kind of like a jungle.

[[...]]

Hey Nerds

A clever person solves a problem. A wise person avoids it. – Albert Einstein

[[...]]

The 1st rule optimization is 'don't do it'.

The 2nd is 'don't do it yet'.

 

 

[[...]]

A complex system that works is invariably found to have evolved from a simple system that worked. A complex system designed from scratch never works and cannot be patched up to make it work. You have to start over with a working simple system. – John Gall (1975, p.71)

[[Es...]]

Hey Nerds

A clever person solves a problem. A wise person avoids it. – Albert Einstein

 

Haha, I can only contribute with words here. Though I’m especially good when it comes to numbers in my bank account. Had to learn some maths and IT for photography and accounting as well. Trial & error... Oh, and I finished some kind of MBA studies in foreign language.

 

It was one of the most stupid accidents in my life. With a little help from my friends, I grasped all those maths, finances, business accounting etc. And graduated with honors... Seriously Figured out I would earn lots of money if I did those studies. And the diploma was helpful

 

"No problem can be solved from the same level of conscioussness that created it." [Albert Einstein]

 

Seems like the guy was pretty smart...

[[Es...]]

 

Threads are like the Hotel California.  You can check out anytime you want, but you can never leave. 

 

Great joke, Bads   ;D "Hotel California" lyrics always made me think of addiction. Oh, and the riffs there are almost as complicated as all those numbers...