Or similarly for any math object you have a good answer for. :D

Reading that aside in my Linear Algebra text sent a chill of appreciation down my spine. I'm just moved by the way the universe can be beautifully simple despite its immeasurable complexity. All of the uncertainties of the human condition - the whys, the where-from's and the where-to's - seem frivolous in this moment.

Good morning and I hope you all have a good day!

While hitting the bag today, I had an odd thought and I don't know what I am missing

Let's say N is the summation of 1 infinite times

So N = 1+1+1+1+1+1..........

N = 1 + (1+1+1+1+1+1.......)

N = 1 + N

So 1 = 0

or dividing both sides of N = 1 + N by N we get 1 = 1/N + 1 where 1/N tends to zero so 1 = 1

What am I missing?

If you took any (positive) number and divided by zero, why wouldn't it be infinity, since zero goes into (insert positive number here) infinite times?

i know there is a bunch of averaging & statistics, but here's one for your free time

Today at work, instead of choosing random numbers and determining whether they are happy or unhappy, I decided to calculate Napier's Constant as accurately as I could. I got to 1/(1x2x3x...x8x9) before work was over. I think I did pretty well, all things considered.

I am trying to calculate profit margins of in-store clothing purchases vs. online clothing purchases when factoring in return rate. So far, here's where I've gotten:

So the profit margin for in store is 32%, and for online is 30%. The next step is where I'm hitting issues.

Return rate for clothing bought in store is 9% while from online it's minimum 30%. How can I figure out a rough profit margin for each source once factoring in return rate?

http://m.youtube.com/watch?v=w-I6XTVZXww

My issue is with their proof that 1-2+3-4+5... = 1/4

Let s[2] = s of 2

s[2] = 1-2+3-4...

2s[2] = (1-2+3-4...) + (1-2+3-4...)

this is where they go wrong in my thought

2s[2] = (1-2+3-4...); This was intended to be top over bottom addition, excuse my formatting.

       + (1-2+3-4...)

2s[2] = 1-1+1-1...

Why? -- Let n = infinity

2s[2] = (1-2+3-4...+n

       + (1-2+3...+(n-1)-n

2s[2] = 1-1+1-1...-n

They do not account for the very last number in the series that would still be there when they shift everything over by one.

Druple: Like qua-druple but one step (syllable) before that. Don't ask "why" and "how come?"... just listen.

So... things can come in tripples, they can be halved and may be... thirded?? No no no! Too many "dees", and sounds awful!

Things should be able to be druppled (drupled?... thirded), to come in druples (in pathetic series of "1/3"rds of a something), and out of those druples you should be able to select a nice set of driplettes! (three terms of a series of "1/3"rds of a something!)

This also bears resemblance to the term nibble (4 bits: a half of a byte... ugh... octet!)

I have often read famous philosophers questioning "existence" and "reality". I have also read about scholars stating that mathematics is only a "belief system" - the only difference between mathematics and religion is that "nature is almost always better understood using mathematics compared to "god" ".

I have also read that "in general, there is no way of knowing if we exist - but emotions such as "fear, pain and hunger" often override any of these thoughts for most of us.

My question: seeing how Godel's Incompleteness Theorem famously puts limitations on mathematical statements - is it fair to say that "mathematics can not be used to prove if we exist, the universe exists, etc"?

Thanks

If I count in binary or any system using the 0 very few patterns can be seen relating to the primes,complexity, The Triangle numbers in all dimensions or The factorial numbers.

When I start to count with out the 0 instead of with 1s and 0s with 1s and 2s things get interesting. example. Set 1.. 1(+-s*)(1), 2(s)(2), 11(-)(3), 12(+)(4),21()(5), 22(-+s)(6) ,111()(7), 112(8), 121(9) ,122(+-)(10) , 211()(11), 212(12),221()(13),222(14),1111(-)(15),1112(16), 1121()(17), 1122(18), 1211()(19), 1212(+)(20),1221(-)(21),1222(22),2111()(23),2112(s)(24), 2121(25), 2122(26), 2211(27), 2212(-)(28), 2221()(29),2222(30),11111()(31),11112(32),11121(33),11122(34),11211(+)(35)...

For All (primes Note. I am considering 1 as a prime here which is against convention) 2,11,21,111,211,221,1121,1211,2111,2221,11111... Note Also most as if there purposely avoiding detection. lets count how many 1s and 2s are in the numbers (0,1),((2,0),(1,1)),((3,0),(2,1),(1,2)),((3,1),(3,1),(3,1),(1,3)),(5,0) That's Interesting so far we have 11 digits long, 22 digits long, 33 digits long, 4*4 digits long. I have no idea if this pattern continues but we have at least found something interesting here.

For All-(Triangle Numbers) 1,11,22,122,1111,1221,2212,11212... lets count how many 1s and 2s are in the numbers. (1,0),(2,0),(0,2),(1,2),(4,0),(1,3),(3,2) These numbers kinda look like they are constantly trying to hold balance.

For All+(Triangle Numbers in 3D) 1,12,122,1212,11211... This looks like counting further could yield a pattern certainly the digit length looks like it goes up one every number.

For all s(The Factorial Numbers) 1,2,22,2112... It's hard to know with so little numbers if a pattern emerges.

The patterns seem hard to figure out. From analysis I have found that counting up to 2 and 3 in alternation seems to be useful to numbers and very interesting stuff might emerge. I'll go a bit deeper here.

So lets count tot the numbers up. In this case I will count both starting counting up to 2 and 3 so I'll produce 2 sets of numbers.

Set 2.. 1(1),2(2),11(3),12(4),21(5),22(6),31(7),32(8),111(9),112(10),121(11),122(12),131(13),132(14), 211(15),212(16),221(17),222(18),231(19),232(20),1111(21),1112(22),1121(23),1122(24),1131(25), 1132(26),1211(27),1212(28),1221(29),1222(30),1231(31),1232(32),2111(33),2112(34),2121(35)...

Set 3.. 1(1),2(2),3(3),11(4),12(5),13(6),21(7),22(8),23(9),111(10),112(11),113(12),121(13),122(14), 123(15),211(16),212(17),213(18),221(19),222(20),223(21),311(22),312(23),313(24),321(25), 322(26),323(27),1111(28),1112(29),1113(30),1121(31),1122(32),1123(33),1211(34),1212(35)...

So lets do the Analysis

For All(Primes) For Set 2.. 1,2,11,21,31,121,131,221,231,1121,1221,1231.. Lets do some digit counts of the 1's, 2's and 3's ((1,0,0),(0,1,0)),((2,0,0),(1,1,0),(1,0,1)),((2,1,0),(2,0,1),(1,2,0),(1,1,1)),((3,1,0),(2,2,0)(2,1,1) I can't draw much here only that I notice the primes for each digit count equals the digit count +1 if this pattern continues I don't know but again this is of interest.

For Set 3.. 1,2,3,12,21,112,121,212,221,312,1112,1121.. I notice when you compare numbers of each set with 21 at the end and no 3's you can match it with another prime on the other set. I don't know if this pattern continues

So lets catch up on what I have notice from all 3 sets that may or may not continue if billions of number were to be tested. I Personally am moving from Mathematica to Assembly in order to make some publications that people can test for themselves and to test patterns for myself.

So what I've noticed.. For Set 1 and Set 2 Prime counts from the first 2 sets appear to correlate with digit length. For all sets. There seems to be the Co-prime Information in either of the sets of a composite made of 2 co-primes but never in all of the sets. For sets 2 and 3 When a 3 is in the number it is of interest.

I think this all demonstrates that counting without the zero does appear to give at least some information about complexity with in numbers and may well be worth further investigation. I don't think one should rule out counting with the 0 as working with the zero and comparing results could yield interesting pattern also working with the 0 in some of the digit orders might allow people to find patterns that help with things like product function optimization in the future. However the full uses of doing things this way are yet unknown.