may I take a turn with an OT question...dealing in reality

[BTMurphy]

So, this question has always been perplexing to me: Let's say my dog Murphy, playing for Boston in the BWI forums league, begins the season 5 for 10 at the plate. Stuck in a space time continuum (this is the reality part), the games continue "forever" and he never again fails to get a hit facing the posters from this board.

My question is this:
He begins the season hitting .500. throughout time his average climbs...20/30 = 666, 90/100 = 900, 990/1000 = 990, 10990/11000 = 9990909 and so on. The average always gets closer to 1000, seemingly indicating he will eventually not only reach an avg. of 1000, but even surpass it. Yet, he will always be 10 hits shy, therefore realizing a perfect average, I thought, is an impossibility. And while I know this to be impossible, that damn number will continually creep closer to 1000.

There are some smart people here on this board. Is there a simple answer to this? I know, I know, the spring game can't get here soon enough....

 

[LionDeNittany]

It's called an asymptote.

This is what limits and derivatives are for.

Never will have a perfect average.

https://en.wikipedia.org/wiki/Asymptote

 

[michnittlion]

Definition of a limit. (x/(x+10)) approaches and continues to get closer and closer to (but never reaches) 1 as x goes to infinity.

 

[Nit Nolte]

Stand in your kitchen. Now step halfway to the wall. Do it again. Forever. You'll approach the wall but never get there.

 

[step.eng69]

It's called an asymptote.

This is what limits and derivatives are for.

Never will have a perfect average.

https://en.wikipedia.org/wiki/Asymptote

Thanks, haven't heard the term used in decades. I knew poor asymptotes once Horatio.

 

[coveydidnt]

say my dog Murphy, playing for Boston in the BWI forums league, begins the season 5 for 10 at the plate. Stuck in a space time continuum (this is the reality part), the games continue "forever" and he never again fails to get a hit facing the posters from this board.My question is this:
He begins the season hitting .500. throughout time his average climbs...20/30 = 666, 90/100 = 900, 990/1000 = 990, 10990/11000 = 9990909 and so on. The average always gets closer to 1000, seemingly indicating he will eventually not only reach an avg. of 1000, but even surpass it. Yet, he will always be 10 hits shy, therefore realizing a perfect average, I thought, is an impossibility. And while I know this to be impossible, that damn number will continually creep closer to 1000.

I realize you probably don't care that much, and the answers above are right, but the question isn't.

He only has 5 at bats where he didn't get a hit. So he will never be 20/30, rather 25/30.

never be 90/100, rather 95/100.

So he will NEVER be 10 hits shy as posed in the question.

 

[coveydidnt]

Don't count Murphy out just yet though. He may still get to a perfect average, and here's how:

Given the scenario as laid out, it's statistically virtually impossible that the 5 times he failed to get a hit were on the up and up. The umpire cheated, the balls were wonky, the pitcher was using some form of amazing PEDs. Something.

There would be all kinds of investigations into those early at bats, and it's very likely that, in a real world scenario (as you describe) that those games would be forfeited or vacated by the other team(s). In other words, those 5 misses would be stricken from the record, ensuring Murphy gets his well-deserved perfect record after all.

 

[anon_1eeb2b426hv3y]

My question is this:
He begins the season hitting .500. throughout time his average climbs...20/30 = 666, 90/100 = 900, 990/1000 = 990, 10990/11000 = 9990909 and so on. The average always gets closer to 1000, seemingly indicating he will eventually not only reach an avg. of 1000, but even surpass it. Yet, he will always be 10 hits shy, therefore realizing a perfect average, I thought, is an impossibility. And while I know this to be impossible, that damn number will continually creep closer to 1000.

There are some smart people here on this board. Is there a simple answer to this? I know, I know, the spring game can't get here soon enough....

I'll bite. You keep getting closer but you'll never get to perfection. I'm confused by your statement "The average always gets closer to 1000, seemingly indicating he will eventually not only reach an avg. of 1000, but even surpass it"--although in no expert in anything like a time-space continuum, which may flip logic on its head.

But what's your question? Its not possible to get better than perfection, and it's not possible to reach perfection if you have an imperfect starting point.

 

[BTMurphy]

I realize you probably don't care that much, and the answers above are right, but the question isn't.

He only has 5 at bats where he didn't get a hit. So he will never be 20/30, rather 25/30.

never be 90/100, rather 95/100.

So he will NEVER be 10 hits shy as posed in the question.

ha! careless mistake on my part. but the point of my question is genuine. I guess I just have trouble accepting that the average will continually inch closer to 1000 (perfection) but never get there. I know It can't, but I'm hung up on the fact that the number between perfection and his current average will become infinitesimally small, yet never reach 1000.

 

[BTMurphy]

It's called an asymptote.

This is what limits and derivatives are for.

Never will have a perfect average.

https://en.wikipedia.org/wiki/Asymptote

that is precisely why I was a History/Poli Sci major!

 

[BTMurphy]

Definition of a limit. (x/(x+10)) approaches and continues to get closer and closer to (but never reaches) 1 as x goes to infinity.

see my response to Liondenittany

 

[jim cummings]

 

[BTMurphy]

Stand in your kitchen. Now step halfway to the wall. Do it again. Forever. You'll approach the wall but never get there.

that just makes this worse!

 

[91Joe95]

ha! careless mistake on my part. but the point of my question is genuine. I guess I just have trouble accepting that the average will continually inch closer to 1000 (perfection) but never get there. I know It can't, but I'm hung up on the fact that the number between perfection and his current average will become infinitesimally small, yet never reach 1000.

Depends how many decimal places you use. If you stop at some point and round, you'll hit it, even though from a non-rounding approach you won't.

 

[LionJim]

1+1/2+1/4+1/8+1/16...=2.

Start with a 2 by 1 rectangle; it has an area of 2. Cut it in half. Then cut one of those halves in half, ad infinitum. You're got a finite sum and at each step you add half of what you're short of 2 by. You'll always be short of 2, but it will always take only a finite number of steps to get as close to 2 as you want.

 

[bjf1991]

^^^^ Exactly

WTF

 

[artsandletters]

1+1/2+1/4+1/8+1/16...=2.

Start with a 2 by 1 rectangle; it has an area of 2. Cut it in half. Then cut one of those halves in half, ad infinitum. You're got a finite sum and at each step you add half of what you're short of 2 by. You'll always be short of 2, but it will always take only a finite number of steps to get as close to 2 as you want.

I was thinking this but didn't know how to articulate it. Thanks, James.

 

[Psychedelic_MackDaddy]

So, this question has always been perplexing to me: Let's say my dog Murphy, playing for Boston in the BWI forums league, begins the season 5 for 10 at the plate. Stuck in a space time continuum (this is the reality part), the games continue "forever" and he never again fails to get a hit facing the posters from this board.

My question is this:
He begins the season hitting .500. throughout time his average climbs...20/30 = 666, 90/100 = 900, 990/1000 = 990, 10990/11000 = 9990909 and so on. The average always gets closer to 1000, seemingly indicating he will eventually not only reach an avg. of 1000, but even surpass it. Yet, he will always be 10 hits shy, therefore realizing a perfect average, I thought, is an impossibility. And while I know this to be impossible, that damn number will continually creep closer to 1000.

There are some smart people here on this board. Is there a simple answer to this? I know, I know, the spring game can't get here soon enough....

It's like riding a horse, but your on backwards. You KNOW where the horse is approaching, but you never actually see where he is.

 

[gamblepsu]

Full disclosure I understand the math. From a practical point though, I would think of this completely the other way. Baseball only goes three decimal places deep. The records would show him with a'perfect' average even though he clearly wasn't.

 

[BTMurphy]

1+1/2+1/4+1/8+1/16...=2.

Start with a 2 by 1 rectangle; it has an area of 2. Cut it in half. Then cut one of those halves in half, ad infinitum. You're got a finite sum and at each step you add half of what you're short of 2 by. You'll always be short of 2, but it will always take only a finite number of steps to get as close to 2 as you want.

I understand. But I just can't accept the idea that he will gain ground with every hit, yet never reach 1000. I know this to be true, but How can he continually close the gap yet never get there. Jim's gif is exactly how I feel. Oh well....thanks to all. Much appreciated