Please Stop Triple Spacing

[DonRocks]

.

[Barbara]

.

The definition of insanity is doing the same thing over and over and expecting a different result. (And I didn't triple space)

[Meaghan]

well, vienna sausages in a can.

[Halloween]

i... can't...help...myself....

[Ferhat Yalcin]

i... can't...help...myself....

can I help you ?

[Scott Johnston]

This is how we do it........

This is how we do it........

This is how we do it........

can I help you ?

can I help you ?

can I help you ?

can I help you ?

can I help you ?

[ManekiNeko]

Poor triple spacing. I hope someone calls it in the morning.

[jparrott]

I believe the standard process for organizing a large chorus of outlaw eunuchs is Try, Pile, Spay, Sing.

[jpschust]

Poor triple spacing. I hope someone calls it in the morning.

Don't pity it. It was asking for it anyways- I mean just look at how much clevage it shows.

[DonRocks]

Actually, if anyone on the board sees a triple-spaced post, would you please cut-and-paste the URL of the post, and PM the poster? Thanks.

And I'm sorry if I'm cranky, but I'm working on a problem right now. In fact, I could use some help.

If anyone can get me the answer, I'll take them out to dinner at Maestro.

Anyway, I need f (4, 2) resolved to an integer value for the following function:

------------------------------------------------------

f (x, y) =

y + 1 ........................ {when x = 0}

f (x-1, 1) ................... {when x > 0 and y = 0}

f (x-1, f (x, y-1)) ........ {when x > 0 and y > 0)

-------------------------------------------------------

It seems pretty simple, so probably won't take too long to resolve. Nevertheless, I can't seem to get the answer, and am willing to pay accordingly to the first person who can get it solved.

First person to PM me the answer gets it.

Thanks!

Rocks

[Seanchai]

Actually, if anyone on the board sees a triple-spaced post, would you please cut-and-paste the URL of the post, and PM the poster? Thanks.

And I'm sorry if I'm cranky, but I'm working on a problem right now. In fact, I could use some help.

If anyone can get me the answer, I'll take them out to dinner at Maestro.

Anyway, I need f (4, 2) resolved to an integer value for the following function:

------------------------------------------------------

f (x, y) =

y + 1 ........................ {when x = 0}

f (x-1, 1) ................... {when x > 0 and y = 0}

f (x-1, f (x, y-1)) ........ {when x > 0 and y > 0)

-------------------------------------------------------

It seems pretty simple, so probably won't take too long to resolve. Nevertheless, I can't seem to get the answer, and am willing to pay accordingly to the first person who can get it solved.

First person to PM me the answer gets it.

Thanks!

Rocks

I was told that there would be no math in this debate ...

[chef4cook]

Actually, if anyone on the board sees a triple-spaced post, would you please cut-and-paste the URL of the post, and PM the poster? Thanks.

And I'm sorry if I'm cranky, but I'm working on a problem right now. In fact, I could use some help.

If anyone can get me the answer, I'll take them out to dinner at Maestro.

Anyway, I need f (4, 2) resolved to an integer value for the following function:

------------------------------------------------------

f (x, y) =

y + 1 ........................ {when x = 0}

f (x-1, 1) ................... {when x > 0 and y = 0}

f (x-1, f (x, y-1)) ........ {when x > 0 and y > 0)

-------------------------------------------------------

It seems pretty simple, so probably won't take too long to resolve. Nevertheless, I can't seem to get the answer, and am willing to pay accordingly to the first person who can get it solved.

First person to PM me the answer gets it.

Thanks!

Rocks

I suck at math. What are the letters doing in there?

[B.A.R.]

The answer is 11.

I am available for dinner Friday.

[jparrott]

f(x, y) =

y + 1 ........................ {when x = 0}

f(x - 1, 1) ................... {when x > 0 and y = 0}

f(x - 1, f(x, y - 1)) ........ {when x > 0 and y > 0)

f(0, y) = 1 + y

Using induction to prove f(1, y) = y +2:

Base case:

f(1, 0) = f(0, 1) = 2 = 0 + 2

Assume for particular but arbitrarily chosen (pbac) k that it is true for (k - 1) then show for k:

f(1, k) = f(0, f(1, k - 1)) = 1+ f(1, k - 1) = 1 + [(k - 1) + 2] = k + 2 QED.

Using induction to prove f(2, y) = 2y + 3:

Base case:

f(2, 0) = f(1, 1) = 3

Assume for pbac k that it is true for (k - 1) then show for k:

f(2, k) = f(1, f(2, k - 1)) = 2 + f(2, k - 1) = 2 + 2(k-1) + 3 = 2 + 2k - 2 + 3 = 2k + 3 QED.

Using induction to prove f(3, y) = 2^{3 + y} - 3:

Base case:

f(3, 0) = f(2, 1) = 5 = 2^{3 + 0} - 3

Assume for pbac k that it is true for (k - 1) then show for k:

f(3, k) = f(2, f(3, k - 1)) = f(2, 2^{3 + k - 1} - 3)

= 2 * (2^{3 + k - 1} - 3) + 3

= 2 * (2^{k + 2} - 3) + 3 = 2^{k + 3} - 6 + 3 = 2^{k + 3} - 3 QED.

Calculating f(4, 2):

f(4, 0) = f(3, 1) = 13

f(4, 1) = f(3, f(4, 0)) = f(3, 13) = 2¹⁶ - 3 = 65533

f(4, 2) = f(3, f(4, 1))

= f(3, 65533) = 2⁶⁵⁵³⁶ - 3

[DonRocks]

2^65536 - 3

Thanks. Now I'll just need you to PM me the integer (not an equation) and I'll take you to Maestro.

And I'll buy you dessert if you PM me the answer to f (4, 3).

Of course, there are more digits in that answer than there are particles in the known universe. And the only number I know of that's larger than this is THE NUMBER OF POSTS THAT I'VE EDITED IN THE PAST 21 MONTHS THAT HAVE BEEN TRIPLE-SPACED.

Please stop triple-spacing!

And if you're curious, click here to learn more about the imposing Ackermann function.

(Oh, and Jake, I have to say ... pretty impressive.)

[jparrott]

Note also that Ack(4, 2) = 2^{2^16} - 3 or F₁₆ - 4, where F₁, F₂, F_n are the Fermat numbers. Fun stuff.

[jparrott]

Thanks. Now I'll just need you to PM me the integer (not an equation) and I'll take you to Maestro.

Binary: 2⁶⁵⁵³⁶ is a 1 with 65536 zeroes after, 2⁶⁵⁵³⁶ - 1 is 65536 ones, so 2⁶⁵⁵³⁶ - 3 is 65534 ones, then a zero, then a one.

Hex: 2⁶⁵⁵³⁶ is 16¹⁶³⁸⁴ or a 1 with 16384 zeroes after, so 2⁶⁵⁵⁴⁶ - 3 is 16383 F's, then one D.

[Antonio Burrell]

Man, should I send it to him in Binary? Or Hex?

You're such a nerd

edited to eliminate triple spacing, I think

[Al Dente]

Note also that Ack(4, 2) = 2^(2^16) - 3 or F_16 - 4, where F_1, F_2, F_n are the Fermat numbers. Fun stuff.

Ack =

[shogun]

well, vienna sausages in a can.

This one time I was at the 7-11 by Foggy Bottom Metro, and there was a guy standing outside with a bag and a soda. He produced a can of Vienna sausages, popped it open, and proceeded to drink the liquid from the can. That accomplished, he ate the sausages.

[B.A.R.]

f (x, y) =

y + 1 ........................ {when x = 0}

f (x-1, 1) ................... {when x > 0 and y = 0}

f (x-1, f (x, y-1)) ........ {when x > 0 and y > 0)

f(0, y) = 1 + y

Using strong induction to prove f(1, y) = y +2:

Base case:

f(1, 0) = f (0, 1) = 2 = 0 + 2

f(1, 1) = f (0, f (1, 0)) = f(0, f(0, 1)) = f (0, 2) = 3 = 1 + 2

Assume for all k = 2 to y-1 that it is true then show for y:

f(1, y) = f(0, f(1, y-1)) = 1+ f(1, y-1) = 1 + [(y - 1) + 2] = y + 2 QED.......................f(4, 2) = f(3, f(4, 1)) = f(3, 65533) = 2^65536 - 3

I stand by 11.

[jparrott]

I stand by 11.

Interesting. I think most folks would double down on eleven.

[jpschust]

Interesting. I think most folks would double down on eleven.

really? on a yo the house has 11.11 percent odds.

[jparrott]

I'll pay for dessert.

Note that Ack(4, 3) has about the same number of digits as the number in the attached file.

Ackerman_4_2.pdf

[DonRocks]

I'll pay for dessert.

Note that Ack(4, 3) has about the same number of digits as the number in the attached file.

I specifically said "PM me the integer" for a reason. This is not a PM.

[jparrott]

Sent.

[Pat]

Sent.

Congratulations if you got something to go through as a PM that's 19,000+ characters long.

[DonRocks]

Well I'll be a son of a bitch. He did it.

[DonRocks]

[ScotteeM]

Is that what shut the site down?

[DonRocks]

Is that what shut the site down?

I just spent ten dollars on additional bandwidth to get us through January. That's an app. Not an applet; an appetizer. Fucking Parrott has no life, chewed up his employer's CPU all afternoon computing a 19,000-digit number, and cost me an order of mozzarella sticks.

[ScotteeM]

I just spent ten dollars on additional bandwidth to get us through January. That's an app. Not an applet; an appetizer. Fucking Parrott has no life, chewed up his employer's CPU all afternoon computing a 19,000-digit number, and cost me an order of mozzarella sticks.

Next time I see you, I'll buy you some!

ETA: I was right to be afraid of all those numbers and letters!

[DanielK]

Well I'll be a son of a bitch. He did it.

Jake, you're my freaking hero.

[ScotteeM]

Maybe we need an admissions test for DR.com: anyone who can solve that sort of problem can't be a member, lest they tie us all up in knots.

And, Don, don't blame yourself for asking the question, when I'm sure you thought no one could answer it.

[johnb]

I just spent ten dollars on additional bandwidth to get us through January. That's an app. Not an applet; an appetizer. Fucking Parrott has no life, chewed up his employer's CPU all afternoon computing a 19,000-digit number, and cost me an order of mozzarella sticks.

I presume those are some of Fabio's Maestro mozzarella sticks.

[Jacques Gastreaux]

I just spent ten dollars on additional bandwidth to get us through January. That's an app. Not an applet; an appetizer. Fucking Parrott has no life, chewed up his employer's CPU all afternoon computing a 19,000-digit number, and cost me an order of mozzarella sticks.

It's the old addage, be careful what you ask for. And also, rocks needed to spend $10 to get us through January, which ends tomorrow. I hope they had internet access at whatever bar he was in when he got word that the site was down.

ETA: And I can just see the shit eating grin that must have been on Jake's face when he hit the send button on that PM.

[CrescentFresh]

It's the old addage, be careful what you ask for. And also, rocks needed to spend $10 to get us through January, which ends tomorrow. I hope they had internet access at whatever bar he was in when he got word that the site was down.

It's tomorrow. And the answer to life, the universe, and everything is actually 42.

[edenman]

Please Stop Triple Spacing, Otherwise Jake Parrott will [make you buy him a meal at Maestro]

[Halloween]

f (x, y) =

y + 1 ........................ {when x = 0}

f (x-1, 1) ................... {when x > 0 and y = 0}

f (x-1, f (x, y-1)) ........ {when x > 0 and y > 0)

f(0, y) = 1 + y

Using strong induction to prove f(1, y) = y +2:

Base case:

f(1, 0) = f (0, 1) = 2 = 0 + 2

f(1, 1) = f (0, f (1, 0)) = f(0, f(0, 1)) = f (0, 2) = 3 = 1 + 2

Assume for all k = 2 to y-1 that it is true then show for y:

f(1, y) = f(0, f(1, y-1)) = 1+ f(1, y-1) = 1 + [(y - 1) + 2] = y + 2 QED.

Using strong induction to prove f(2, y) = 2y + 3

Base cases:

f(2, 0) = f(1, 1) = 3

f(2, 1) = f(1, f(2, 0)) = f(2, 0) + 2 = 5 = 2(1) + 3

Assume for all k = 2 to y-1 that it is true then show for y:

f (2, y) = f(1, f(2, y-1)) = 2 + f(2, y-1) = 2 + 2(y-1) + 3 = 2 + 2y - 2 + 3 = 2y + 3 QED.

Using strong induction to prove f(3, y) = 2^(3+y) - 3 [where 2^x denotes 2 raised to the power of x]:

Base case:

f(3, 0) = f (2, 1) = 5 = 2^(3+0) - 3

f(3, 1) = f (2, f(3, 0)) = f (2, 5) = 13 = 2^(3+1)-3

Assume for all k=0 to y-1 that f (3, k) = 2^(3+k) - 3. Now prove for y.

f(3, y) = f(2, f(3, y-1)) = f(2, 2^(3+y-1) - 3) = 2{[2^(3+y-1)] - 3] + 3

= 2* {[2^(y+2)] - 3} + 3 = 2^(y+3) - 6 + 3 = 2^(y+3) - 3 QED.

f(4, 0) = f(3, 1) = 13

f(4, 1) = f(3, f(4, 0)) = f(3, 13) = (2^16)-3 = 65533

f(4, 2) = f(3, f(4, 1)) = f(3, 65533) = 2^65536 - 3

Uhhhh. Que???!!!

[jparrott]

And I can just see the shit eating grin that must have been on Jake's face when he hit the send button on that PM.

Actually, I was quite amused that such a tool existed!

Fucking Parrott has no life

Guilty. Or are you talking about my long-lost second cousin, eleven times removed?

chewed up his employer's CPU all afternoon computing a 19,000-digit number

Actually, it took about a minute on a Dell Latitude D505 laptop.

cost me an order of mozzarella sticks.

I wonder. What would Vincent Feraud propose alongside some nice fritti da mozzarella?

[crackers]

If this dish is on the menu six months from now at $20, and has the same quantity and quality of ingredients, I'll run down K Street with no clothes on during rush hour.

Cheers,

Rocks.

Go Jake! Enjoy your dinner at Maestro (go sooner rather than later, I would advise.) Aren't you glad he wagered a meal at Maestro, and not the above? BTW, has anybody checked the menu at Blue Duck Tavern recently?

[jparrott]

Sadly, this particular meat-and-two-veg is not on the current online menu.

[DanCole42]

This whole thing goes well beyond the Algebra 2 level of education I attained in high school.

e^i(pi) = -1

I have a file on my computer of pi to 10 million digits. I like to see how many times my phone number appears in it (twice), and friends' birthdays.

Mmmmmmm.... pie.....

[Jacques Gastreaux]

Jake, I'm glad to see that that MIT education of yours is starting to pay off.

ETA: There are 19,729 digits in that number. It takes up 6 pages in a Word document.

[ol_ironstomach]

That, and be glad that Rocks didn't pose his (solvable) challenge using sets of timed Putnam competition questions...

(eta: the decimal calculation runs in about five seconds flat using this Java-based bignum calc)

[Barbara]

Question: Just what exactly is wrong with post #31 on this thread?

[jparrott]

ETA: There are 19,729 digits in that number. It takes up 6 pages in a Word document.

I thought I had posted that earlier, but it was removed in a fit of pique--the moderator spilled Vietnamese beef stew on his coarsely-knit polo shirt.

Note, of course, that you can calculate the number of digits without writing out the number by taking the base-10 logarithm:

log₁₀2⁶⁵⁵³⁶ = 65536 * log₁₀2 ~= 65536 * 0.30103 ~= 19728.3

and rounding up.

[cjsadler]

Nerds and Rachael Ray lust-ers... I knew it!

[RRSmith]

THE NUMBER OF POSTS THAT I'VE EDITED IN THE PAST 21 MONTHS THAT HAVE BEEN TRIPLE-SPACED.

Please stop triple-spacing!

OK, I'm confused. We were PM'd that we were guilty of triple spacing. Are we talking actual triple spaces, or are we talking ellipsis'? I know I'm a big ellipsis user. Is this what is causing all the grief?

[Barbara]

OK, I'm confused. We were PM'd that we were guilty of triple spacing. Are we talking actual triple spaces, or are we talking ellipsis'? I know I'm a big ellipsis user. Is this what is causing all the grief?

Answer: Rocks himself ( ) triple-spaced in post #31. It fascinates me that NOBODY, including Rocks his ownself, picked up on this. Thus making this whole subject completely irrelevant.

ETA: WELCOME, RRSMITH, to our merry, if somewhat confused, band.