2 + 2 = 5

[Selta]

You lose information with you round 1/3 to 0.333 but not 0.333333 with infinite number of 3's. Because 1/3 IS 0.3333 w/ infinite number of threes. Unless you can argue that 1/3 is 0.33333333.....4.

And if 1/3 = 0.333333 w/ infinite number of threes, then that means 1/3 + 1/3 +1/3 should also equal to 0.333333 + 0.33333 + 0.33333 each with infinite amount of 3's. Because, like I said, 1/3 IS 0.333333 w/ infinite number of threes.

I know that 1/3 + 1/3 + 1/3 = 3/3, and anything divided by itself (other than 0 and infinity) is 1. So 3/3 = 1, thus 1/3 + 1/3 + 1/3 = 1. But one can also argue, see above paragraph, how 1/3 is exactly same as 0.333 w/ infinite number of 3's. And 0.3333 + 0.3333 + 0.3333 (each number w/ infinite number of 3's) is equall to 0.9999 (w/ infinite number of 9's), which does not equal one.

Enlighten me, how would you apply integration to that adding numbers? (no sarcasm)

And there's your rounding. Highlighted for your enjoyment, folks.

 

[AmazingGracePlayer]

And there's your rounding. Highlighted for your enjoyment, folks.

Making fun my argument doesn't do you any good. I did not round once. 1/3 equals 0.33333 with infinite threes, I gave you EVERY SINGLE DIGIT of that decimal, there's no rounding. Are you sure you got straight A's in college calculus? And how about my question, how would you use integration to add 3 numbers?

 

[somethingsin]

the thing is, I do believe .0.99999 (repeating) == 1

If they aren't equal there must be some number a > 0 so that 0.9999999999..... + a == 1.

however, there is no such number, as there are always more 9's to ensure that 0.9999999 + a > 1

 

[Selta]

Making fun my argument doesn't do you any good. I did not round once. 1/3 equals 0.33333 with infinite threes, I gave you EVERY SINGLE DIGIT of that decimal, there's no rounding. Are you sure you got straight A's in college calculus? And how about my question, how would you use integration to add 3 numbers?

What an integral is is addition. Basically put.
And, again, you have to ROUND 1/3 to 0.333 repeated. It does NOT NOT NOT NOT equal 0.33 repeated. You lose a function of accuracy when you round (convert, change to, go from one to another) from fractions to decimals. However you want to put it, the verbage doesn't matter.
Going from 1/3 to 0.333 is basically, a guess. We know it's one third of one, but the numbering system we use can't express infinity at all, and on top of that, as expressed eariler, YOU'RE ROUNDING.
Ask your teacher if when you "convert" from fractions to decimals, if you ever have to take rounding into account. Depending on their background, they'll give you a solid answer. I'm actually surprised s/he brought up this non-"fact".

Edit:
I was not making fun of your argument. I was pointing out that you're rounding when you say 0.3333 = 1/3, when in fact, it does not. And, also, you may look to be a bit more polite when asking for information from someone, next time. Yes, I'm sure I got straight As in calc., I have the transcripts and even papers to prove it, since my one professor said that she has only handed out less than 25 A's in her entire teaching career - and I got a plaque out of it .
Edit 2:
You can easily see how an integral is a summation. The sign for an integral resembles a script "S", enlongated. S stands for, of course, summation. I thought you got a 5 on some calc exam?

 

[Loose Cannon]

Got to admit, when I saw the heading of this thread, I was afraid someone one beat me to it, but so far you guys are arguing mathematics. Big relief!!

2+2=5 is my contribution to society, you see. At least I hope it to be. And all of you, the most exalted members of TalkBass, may join me in my crusade to establish this phrase into common everyday usage. All you must do, is next time you speak of someone who came to the wrong conclusion,or imagined there to be more to a situation than the facts supported, simply say, " He/She put two and two together and came up with five!"

I believe we can change the world if we keep at it, and eventually everyone will start to use this phrase. When that day comes, we will remember where it all began, right here in the hallowed halls if TalkBass. Thank you. Go forth and multiply.

 

[ThatGermanDude]

aren't you guys saying the same thing over and over again?

or am i missing somthing?

 

[lemur821]

.9999... does too equal one, as long as you're dealing with real numbers. It's just an alternate way of writing 1 (just the same as 1/3 is another way to write .3333...). Since the set of real numbers does not include infinite quantities (although the set itself is infinitely large) or infinitesimal quantities (infinitely small) there can be no quantities between .9999... and 1. Therefore they are alternate ways to write the same number.

If you want to involve imaginary numbers, all bets are off.

 

[AmazingGracePlayer]

What an integral is is addition. Basically put.
And, again, you have to ROUND 1/3 to 0.333 repeated. It does NOT NOT NOT NOT equal 0.33 repeated. You lose a function of accuracy when you round (convert, change to, go from one to another) from fractions to decimals. However you want to put it, the verbage doesn't matter.
Going from 1/3 to 0.333 is basically, a guess. We know it's one third of one, but the numbering system we use can't express infinity at all, and on top of that, as expressed eariler, YOU'RE ROUNDING.
Ask your teacher if when you "convert" from fractions to decimals, if you ever have to take rounding into account. Depending on their background, they'll give you a solid answer. I'm actually surprised s/he brought up this non-"fact".

Edit:
I was not making fun of your argument. I was pointing out that you're rounding when you say 0.3333 = 1/3, when in fact, it does not. And, also, you may look to be a bit more polite when asking for information from someone, next time. Yes, I'm sure I got straight As in calc., I have the transcripts and even papers to prove it, since my one professor said that she has only handed out less than 25 A's in her entire teaching career - and I got a plaque out of it .
Edit 2:
You can easily see how an integral is a summation. The sign for an integral resembles a script "S", enlongated. S stands for, of course, summation. I thought you got a 5 on some calc exam?

I know what integrals are, it's pretty much 50% of calculus (don't argue about that, it's meant to be a joke). But how does 0.33333 with 3 repeating not equal to 1/3?
What is 1 divided by 3? I say it's 0.33333 with countless 3's.

I don't like to start fights. We were having a pretty good debate (no matter how pointless it is, it's 3 1/3's, until you said something like this...

And there's your rounding. Highlighted for your enjoyment, folks.

Everyone must love reading my rounding then! And everyone must love laughing at my rounding. How can I be polite anymore?

 

[lemur821]

Everyone must love reading my rounding then! And everyone must love laughing at my rounding.

I like your rounding. Er... actually I didn't see any rounding. But I'm sure you're good at it.

 

[Brad Barker]

That's reminds me of something my teacher taught me...

Since 1/3 is 0.33333333 (3 repeating), then 1/3 +1/3 +1/3 should equal 0.9999999 (9 repeating) but not 1. It does equal 1 when you round up, but we are talking about exact values here. It's impossible for three 1/3's to add up to one unless one of the 1/3 is 0.333333333334. But 1/3 is not 0.33333333334, it's 0.333333333333 with three repeating, there's no fours involved in there. So therefore 1/3 + 1/3 + 1/3 = 0.9999999 (9 repeating). Anyone care to prove that wrong?

the problem is that 0.99999999... (9, repeating) is EXACTLY equal to 1!

your little example is a decent heuristic way to see it, but let's do it a little more rigorously.

suppose 0.9, with the 9 repeating infinitely, is a number.

let x = 0.9, with the 9 repeating.

consider 10*x:

10*x = 9.9, with the 9 repeating.

now consider 10*x - x:

9.9 (9 repeating) - 0.9 (9 repeating) = 9.

so we have...

9*x = 9.

thus x=1.

but x WAS 0.9 (9 repeating).

so the two numbers are the same.


this has to do something with "the completeness of real numbers," although i don't like math NEARLY enough to read anything about it.

 

[Brad Barker]

I've been saying that forever. But, it's not true.
1/3 is .333 repeating forever. In essence, it doesn't matter, since you get so close to 1, that it is 1. Basically, it's a summation notation. I proved it in calc 3 at one point using an integral .
And, you also have to realize, when you go from fractions to decimals, there's rounding error . 1/3 + 1/3 + 1/3 = 1. 0.333333 x 3 does not, excatly equal one.

why would you do that in calc 3?

get back to computing curls, you!

 

[Selta]

why would you do that in calc 3?

get back to computing curls, you!

Proved it to myself, as I had nothing better to do.

Such a life I lead. Makes me all the more glad, looking back, that I decided I didn't want to be an engineer .

 

[Geoff St. Germaine]

the problem is that 0.99999999... (9, repeating) is EXACTLY equal to 1!

your little example is a decent heuristic way to see it, but let's do it a little more rigorously.

suppose 0.9, with the 9 repeating infinitely, is a number.

let x = 0.9, with the 9 repeating.

consider 10*x:

10*x = 9.9, with the 9 repeating.

now consider 10*x - x:

9.9 (9 repeating) - 0.9 (9 repeating) = 9.

so we have...

9*x = 9.

thus x=1.

but x WAS 0.9 (9 repeating).

so the two numbers are the same.


this has to do something with "the completeness of real numbers," although i don't like math NEARLY enough to read anything about it.

THANK YOU! Up until getting to your post I was losing my mind with this "debate". I was worried I was going to have to write something.

 

[Brad Barker]

THANK YOU! Up until getting to your post I was losing my mind with this "debate". I was worried I was going to have to write something.

for the record, i got both a 5 on my ap calculus ab exam (no bc offered at my school, although i should've taken that exam instead--i knew the material well enough) and have straight a's through six semesters of college.

...just in case proof by intimidation happens to work nowadays.

(then there's that left half of my custom user title. )


when i TA'd for my school's math for liberal arts majors class last semester, there was a part on the real numbers where my students had to deal with infinitely repeating decimals. namely, converting them into fractions.

i hadn't dealt with that topic formally in my life before then, nor was there a section in the textbook that covered it. what i should've done was talked to my boss (the professor) about how she wanted me to teach it (and learn how she covered it in her class).

instead, i spent a few minutes coming up with a way to do it on my own. in retrospect, the way the teacher did it was probably much more "clean," but my students liked my method well enough.

but this semester, i learned the more formal way of doing things, which i did in my earlier post, in my numerical analysis class, when we learned how to convert fractions into decimals in base 2.

(the point was to get to relative and absolute error, which comes about by rounding, say, 1/3 to 0.3333.)


anyway, ....carrots?

 

[Brad Barker]

Proved it to myself, as I had nothing better to do.

Such a life I lead. Makes me all the more glad, looking back, that I decided I didn't want to be an engineer .

wait, what're you doing now?

 

[Selta]

wait, what're you doing now?

Not being an engineer?

All kidding aside, I now play with computers and basses to support myself.

 

[Geoff St. Germaine]

for the record, i got both a 5 on my ap calculus ab exam (no bc offered at my school, although i should've taken that exam instead--i knew the material well enough) and have straight a's through six semesters of college.

...just in case proof by intimidation happens to work nowadays.

(then there's that left half of my custom user title. )


when i TA'd for my school's math for liberal arts majors class last semester, there was a part on the real numbers where my students had to deal with infinitely repeating decimals. namely, converting them into fractions.

i hadn't dealt with that topic formally in my life before then, nor was there a section in the textbook that covered it. what i should've done was talked to my boss (the professor) about how she wanted me to teach it (and learn how she covered it in her class).

instead, i spent a few minutes coming up with a way to do it on my own. in retrospect, the way the teacher did it was probably much more "clean," but my students liked my method well enough.

but this semester, i learned the more formal way of doing things, which i did in my earlier post, in my numerical analysis class, when we learned how to convert fractions into decimals in base 2.

(the point was to get to relative and absolute error, which comes about by rounding, say, 1/3 to 0.3333.)


anyway, ....carrots?

We had to prove that 0.99999.... = 1 in my first year linear algebra class on the final exam.

 

[XavidmanX]

Back to the poor man's original question of 2+2=5...or did we get to that already?
It can be done but somewhere in the proof you divide both sides of the equation by (a-b) after already stating that a=b, thus dividing by zero and causing the paper and pencil to explode.
I've taught math (everything from pre algebra to pre calculus and calculus) and frankly, if .9999999999... = 1, I could care less, unless, the irrefutable proof of such problem would make me a millionaire and owner of an endless supply of Roscoes and MTD's. I just wanna play bass!

 

[Geoff St. Germaine]

Back to the poor man's original question of 2+2=5...or did we get to that already?
It can be done but somewhere in the proof you divide both sides of the equation by (a-b) after already stating that a=b, thus dividing by zero and causing the paper and pencil to explode.
I've taught math (everything from pre algebra to pre calculus and calculus) and frankly, if .9999999999... = 1, I could care less, unless, the irrefutable proof of such problem would make me a millionaire and owner of an endless supply of Roscoes and MTD's. I just wanna play bass!

Well, then you'd know that most mathematical proofs aren't going to get you a million dollars. Invalid Link Removed can though.

 

[Jeff Moote]

"However, the less well known equation 2 + 2 = 5 also has a rich, complex history behind it. Like any other complex quantitiy, this history has a real part and an imaginary part...."

why would you do that in calc 3?

get back to computing curls, you!

I cannot put into words how completely useless div, curl and grad seemed in calc 3, and how incredibly necessary I know they are now that I've had my class that applies them. It's my Calc 3 prof's fault for not covering enough physical applications!!

THANK YOU! Up until getting to your post I was losing my mind with this "debate". I was worried I was going to have to write something.

I was thinking the same thing. Thank goodness Brad finally put an end to the madness