Ehrlich

ab+2a+3b+6=3*(b+2)+ab+2a=

3*(b+2)+a*(b+2)=

(a+3)*(b+2)

you cant. Lets take for example an equation of the form a₀+a₁*x^t₁+a₂*x^t₂+a₃*x^t₃..........a_n*x^t_n=0,

where t₁ 2 3<..... n<0

Now multiply by x^-t₁ and get: a₀*x^-t₁+a₁+a₂*x^t₂-t₁+a₃*x^t₃-t₁+a₄*x^t₄-t₁+a₅*x^t₅-t₁..........a_n*x^t_n-t₁=0

the equation is exactly the same, no solution was added (you can check it)

So it doesnt tell anything about the answer.

I just answered some guy's question about how to convert 3.1415 to binary. heureka posted the algorithm. You can check it.

Now, I believe you know how bases work-

suppose we are writing using base n. That means we have n digits that represent numbers:

0, 1, 2, ......n-1

for example, if n=2. we have 2 digits- 0 and 1.

Lets call the first digit the main digit (for example, the main digit in 11001010110 be 0, in 345 it will be 5 and so on)

If the digit d is K places to the left of the main digit, its value will be the base multiplied by itself K times, then multiplied by the digit. if the base is N it means the value will be d*N^K. It also means that if the digit is K places to the right of the main digit, its value will be d*N^-K=d/(N^K)

for example, if our base is 10, then the value of the marked digit in 0.007 will be 7*10^-3=7/(10³).

If our base is 2, it means the value of the marked digit in 0.01 will be 1*2^-2=1/(2²)

So, if we want to convert 3.141592 to base 2, we have to use those rules. 3.141592 (base 10)~~11.0011

Unfortunately for you, pi is irrational, meaning we cant write it with a finite number of digits (i know you didnt want me to do that but i just had to say that)

you wanted me to write 3.141592 in base 2, and im afraid to tell you we cant write this rational number with a finite number of digits either! but we CAN write it as a Repeating decimal. why? because if you dont want a fraction to be a repeating decimal (lets say the fraction is m₁/m₂) then after reducing the fraction you need all of m₂'s factors to be factors of the base N as well. It doesnt work with 141592/1000000, but we can write it as a repeating decimal.

Can you to that?

Oneof the things that puzzled me is that the lecturer said a vector can be expressed by a function, or that a function can be represented by a vector, or that functions and vectors are the same. Im not quite sure tho.

Lets see. So we have a 4-digit palindrome. that means the first digit and the last digit are the same. it also means the second digit and the third digit are the same. lets call the first one a, the second- b, thhrd- c, and fourth- d

a=d

b=c

we know that a*1000+b*100+c*10+d=a*1000+b*100+b*10+a=a*1001+b*110 is divisible by 7.

we know that 1001 is divisible by 7 (1001/7=143), and that 110 is NOT divisible by 7. that means we need b to be divisible by 7 (because a number divisible by 7+a number NOT divisible by7=a number NOT divisible by7

and

a number divisible by 7+a number divisible by 7=a number divisible by 7

the first digit of the number has to be between 1 and 9, and the other digits have to be betwee 0 and 9. meaning 1<=a<=9 and 0<=b<=9. if we need b to be divisible by 7 there are 2 options for b- 0 or 7. there are 9 options for a because a*1001 will always be divisible by 7 and 1<=a<=9 leaving 9 options for a.

2*9=18

so there are 18 4-digit palindromic numbers are divisible by 7

Lets assume a+b>2

a>2-b

Therefore,

a³>(2-b)³=8-b³+6b²-12b

We know a³=2-b³ (because a³+b³=2)

2-b³>8-b³+6b²-12b ........add (b³-2)------>

0>6+6b²-12b..........divide by 6----------->

0>1+b²-2b=(b-1)²

but (b-1)² cant be smaller than 0!

we could also find the smallest number that is bigger than a+b if we called 2 'c₁' and the limit for the largest number 'c₂' to get a more general solution for every c₁.

a³+b³=c₁

a³=c₁-b³

we want to find the smallest c₂ that is bigger than or equals to a+b. (a+b<=c₂)

a<=c₂-b -------->

a³<=c₂³-b³+3b^2*c₂-3b*c₂² ---------->

c₁-b³<=c₂³-b³+3b²*c₂-3b*c₂² --------->

0<=c₂³-c₁+3b²*c₂-3b*c_2²=3c₂*[(b-(c₂/2))²+c₂²/3-c₁/c₂*3-c₂²/4]

so now there are 3 options-

1. c₂ is negative, therefore we want [(b-(c₂/2))²+c₂²/3-c₁/c₂*3-c₂²/4] to always be negative (because negative*negative=positive) but we cant because b can be as big as we want. meaning we cant do that.

2. c₂=0, meaning c₁=0. but c₁ is a constant that cant be determined by c₂.

3. c₂ is a positive number, meaning we want [(b-(c₂/2))²+c₂²/3-c₁/c₂*3-c₂²/4] to be positive always (because positive*positive=positive)

we know the minimum value for (b-(c₂/2))²  is 0. so we need c₂²/3-c₁/c₂*3-c₂²/4 to be bigger than 0.

c₂²/3-c₁/c₂*3-c₂²/4=c₂²/12-c₁/c₂*3>=0 multiply by 3*c₂-------------->

c₂³*1/4-c₁>=0

therefore, c₂>=(c₁*4)^1/3 

we can also use calculus for this question

a=x, b=(c₁-x³)^1/3

f(x)=x+(c₁-x³)^1/3

f'(x)=1-3*x²/3*(c₁-x³)^1/3-1=1-x²(c₁-x³)^-2/3=0 ----------------->

x²(c₁-x³)^-2/3=1 multiply by (c₁-x³)^2/3 -------------------->

x²=(c₁-x³)^2/3---------------------->

x⁶=(c₁-x³)²=c₁²+x⁶-2*c₁*x³------------------>

2*c₁*x³=c₁² divide by (c₁*2) ------------->

x=(c₁/2)^1/3

f((c₁/2)^1/3)=(c₁/2)^1/3+(c₁-c₁/2)^1/3=2*(c₁/2)^1/3. this is a more accurate answer for the maximum value of a+b.

Ok. The browser restarted a few times after writing my answer. Im not mentally stable right now, but ill try.

Ehrlich, you should read this post:  https://web2.0calc.com/questions/to-mr-andre-massow#r1

 

This is 14-year-old Dragonlance, articulating the nuances of web2.0calc’s social structure, in response to (who we now know as) our Blarney Banker. The Banker usually rants, but here he was even-tempered, probably because he was addressing Herr Massow.  

 

DL acknowledges and explains the obnoxious elements of any social forum that allows for unrestricted access and speech. 

 

“There many visitors who come and go as they please and the troll don’t collect his fare most of the time. There are some here who use the sidewalk instead of the bathroom, but that is true in any city or kingdom.”

 

In his final statement, he gives the Blarney Banker a valid suggestion:  “If you can’t stand this then go somewhere else. There are lots of sites you can answer questions and learn maths”

 

Ehrlich, this suggestion will work for you too.

Im not forcing anyone to do anything. I simply suggested ideas. Im not going to track down anyone for not accepting my plan. I just think its going to improve the site. thats all. I guess im going to leave.

What DL says is true; there are many math forums. Some are very good –with a few exceptions, they are mostly oriented to advanced education, but most orientated to lower level math are derelict and desolate, with many questions unanswered or answered incorrectly or poorly. These sites may have no social commentary, but they also have very little math commentary and that is supposed to be their purpose. They are little math ghost towns.  Guess what they all have in common. ... They are oriented to middle and high school students.  If the social part of the forum is restricted, the middle and high school members will just leave. Many of the college students will leave too, then this site will become a little ghost town (again).  

 

There is not another math forum like web2.0calc.com anywhere on the web. The undesirable social elements are a byproduct of this math forums unique nature. It is reasonable to expect this in any social environment--whether in a virtual or real world. It is also reasonable to expect some tolerance for young persons who are learning how to communicate socially, who are learning the different between assertive and aggressive behavior, and other allowable limits of social boundaries. This is a slow process. Their little brains are just starting to develop enough to have an advanced sense of ethics.

 

Here’s an example in progress:   https://web2.0calc.com/questions/i-think-its-important-continued

Oh, the age-old question. "Are ethics more important than knowledge?". Its not the first time i hear this. Ive never said ANYTHING about knowledge being more important than ethics. i dont think knowledge is more important than ethics, and i think it has nothing to do with what i posted. i dont want to "get rid" of the ethical/social aspect of the forum. you are more than welcomed to check every embarrassing post ive ever posted. you wont find any.

 I just want to get it somewhere else, to another forum, just because it feels messy when scrolling up or down the main page. the forum wont have to become a "ghost town" as you call it. Besides, i think the link you said is alittle irrelevant. the post in this link is different than mine, and discusses different things.

Here, Cole2 is in the midst of an ethical dilemma.  To post or not to post, that is the question. Cole decides to post, with apologies to Sir CPhill, who has (apparently) taught and awakened him to his responsibilities for social ethics.  Kudos to Sir CPhill: Learning ethics is more important than learning mathematics. I do not believe anyone wants his or her kid throwing poo while quoting the Pythagorean Theorem. Next to parents, it is the teachers and tutors who guide children to reasonable dispositions in ethical behavior.

 

Cole2 is a kid. You seem older—not by much, but I suppose you’re in college, and you’ve made several social posts on here. 

 

https://web2.0calc.com/questions/w-f_6#r4

https://web2.0calc.com/questions/fvbnmhyjnm#r3

https://web2.0calc.com/questions/all-mods-melody#r3

https://web2.0calc.com/questions/joke_6#r2

. 

The first three are crude juvenile comments and there is nothing socially redeeming nor funny about them.  Isn’t it hypocritical to complain about social posts when you do this yourself? Your posts offend a lot more members than the hyperkinetic greetings of the younger members.

Well done detective. you got me.

But i can explain. May i share my sad story with you?

When i wasw born, everything looked fine. I looked healthy on the outside, and everything was on place.

A few months later, my mother realized something is wrong. She went to the doctor, and after a quick MRI scan they knew it all. Something was missing on the inside. Very few people know about this, but there is a part in the brain responsible for us being funny. But i didnt have that one. Later, in my school, i couldnt find any friends. nobody wanted to talk to me. i was lonely and desperate, and i still am.

You're right, im not funny. those pseudo-jokes are awful. the fourth one is a joke i coppied from a website! its not even mine!

my point is it doesnt have to be funny to be relevant. What im talking about is spamming the main page, or spamming on an important question. it makes it messier. im sure there are some types of people we all can agree that are spammers. but the way i see it, im not a spammer. that question is irrelevant anyways, and meant for irrelevant things.

 Here are a few comments on your blarney.

 

“ and adding another forum is no big deal.”

 

Well then, just write the code and submit it to Herr Massow for his approval. I’m sure he’ll be impressed!

 

CONS: none (The way i see it)

 

For this one, I’ll borrow an answer from Dragonlance’s responses to the Blarney Banker’s criticism of the site calculator. (One of the funniest posts on here).  “Well your eyes aren’t very good. Maybe you need glasses. A brain would help too.”  https://web2.0calc.com/questions/melody-what-are-some-of-the-amazing-things-that-your-ohline-can-do-and-that-my-hp-scientific-calculator-can-t-do#r3  

 

PROS: saves time.

i think one of the worst thing a site can be is a human- dependent site.

And this is not the only way to do this, obviously, but i think its a way you can (and should) use.

 

I can almost hear Rod Serling (or Naus) now, “Submitted as an on-topic consideration, Mr. Ehrlich: formerly a maker of magic bullets for troubleshooting; now, extinguished by his own creation in the early days of artificial unintelligence.”  

Well then, could anyone send me the current code? i would love to try.

If you have some cons to share with me about my i dea, i would love to hear them. im not saying my idea is perfect.

Your hash tag says “#MakeWeb2.0CALCGreatAgain” The fact is this site is Great and has been for more than the last three of its five years. That started when a trained and skilled teacher signed on. That teacher is Melody. She along with CPhill, Alan, and a few others created a reasonably stable virtual social environment where children and adults can learn mathematics, (physics and chemistry too), along with social etiquette.  it's amazing how well it has worked without your help! I think it also amazing how a 14-year-old seems to recognize this, ("They learn maths on here and maybe some manners too."),  when so many “adults” seem oblivious.

I didnt say its not great. Just like what one of trump's party's member said about him, youre talking this quote too seriously. I didnt mean its not great. all im saying is we can make it better.

Now for an example of a funny social post: Here is Naus trolling Melody for a Valentine’s Day greeting. Naus appends this to the post in response to solicited suggestions from Melody.  Melody found this very funny. Who wouldn't find this funny and endearing?  I sure do. 

 

Here’s another dog that didn’t get what he wanted either. 

 

https://www.youtube.com/watch?v=nGeKSiCQkPw

 

Aside from being very funny, this is proof that every SOB doesn't get what he wants all the time.

I cant ignore the fact youre trying to... i cant really put my finger on it.... demonize me? no, that is a too strong term. Every time you answer my questions, youre insulting me every few paragraphs like you're sprinkling spices. Same applies to Naus and DL. they seem to ignore what the person is asking and take it the worst way. Your insults dont impress me. They only tell you arent really treating me as you would treat every other person. Youre squeezing the worstout of my posts and acting as if this is what i meant, then criticizing me in the form of insults.

and before you post an answer with a quote of mine calling chaos-something-something's (its ctc if im not mistaken) posts b******t, they are. unlike you, im trying to treat it with respect. unfortunately, i just cant treat HIM the way i treat you or other people because he doesnt make any sense.

Well, atleast you are being rational.

Im not a "mathbitch". I dont do it because math is "sacred" and other things arent. I dont care about your hobbies, i dont care if you love math, hate math, i simply dont care. but people need to stick to the topic of the forum. its called "WEB2.0CALC" for a reason, d**n it. If you want do talk about other things, open a new forum, that's what my alternative is. Unfortunately, you turned down my offer, because theres a "off topic" button, and you could "simply" flag every post that is irrelevant. Of course by that you have to go over the forum again and again, but for some reason its more effective, or more 5-years-old-friendly. Couldnt you open that forum? couldnt you ATLEAST give them the option to flag themselves as irrelevant if they feel so? you really are beating your head against the wall for no reason.

I didnt get the whole "Batshit stupid" thing. Go ahead, if thats what you think, flag me.

I also think you've misunderstood me. When you read my posts you're probably picturing an old angry man slamming his keyboard. Im simply proposing a better way to arrange this forum.

There is one thing that is clear: The Clown Prince is dealing with his chaotic dark passengers well more efficiently than you are dealing with yours. You are making yours worse!

 No thanks. I dont need you to tell me how to live my life. Im not asking you to know my, because you wont. Dont your energy writing idiotic sentences.

The funny thing is, Mystical jaycat Had another solution that doesnt rely on you- she opened a discord chat. Why cant you go there instead? is it too hard to type a few words and click your mouse twice?

I come out evil and annoying in your comment, while other arent, because they seem positive or because it seems they are very nice.

Theres one thing i ask you to do. Enter the discord chat mysticalcat added, scroll all the way up and read.