Ttyjukl

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I’ve officially counted to infinity!

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2

$begingroup$

It’s been a while since my last post since school, work, and family have kept me incredibly busy. I have another puzzle though and as always I wish you the best of luck.

Sarah called me today and explained that she had counted to infinity. I shrugged and said it was impossible. She said that since I didn’t believe her, she would do it again, and this time in only ten minutes. I thought it was impossible but she did it right before my eyes!

How did Sarah count to infinity in only ten minutes?

Clarifications

Sarah indeed counted all the way to infinity.

riddle mathematics knowledge story

share|improve this question

edited 1 hour ago

PerpetualJ

asked 1 hour ago

PerpetualJPerpetualJ

4,130547

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome back! :)
  $endgroup$
  – Mr Pie
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Oh, and just so there is no confusion here, does Sarah mean that she counts to infinity as opposed to counting towards infinity? There is a difference, and I feel like this is an important, but subtle, detail to address.
  $endgroup$
  – Mr Pie
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @MrPie All the way to infinity!
  $endgroup$
  – PerpetualJ
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  This question feels a bit too broad. Are you sure there's one demonstrably correct answer to this one?
  $endgroup$
  – PiIsNot3
  45 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @PiIsNot3 I’m pretty sure there is one way to count to the end of an infinite set in a finite time span.
  $endgroup$
  – PerpetualJ
  22 mins ago
  

  
  
  
  

 | 
show 1 more comment

2

$begingroup$

It’s been a while since my last post since school, work, and family have kept me incredibly busy. I have another puzzle though and as always I wish you the best of luck.

Sarah called me today and explained that she had counted to infinity. I shrugged and said it was impossible. She said that since I didn’t believe her, she would do it again, and this time in only ten minutes. I thought it was impossible but she did it right before my eyes!

How did Sarah count to infinity in only ten minutes?

Clarifications

Sarah indeed counted all the way to infinity.

riddle mathematics knowledge story

share|improve this question

edited 1 hour ago

PerpetualJ

asked 1 hour ago

PerpetualJPerpetualJ

4,130547

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome back! :)
  $endgroup$
  – Mr Pie
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Oh, and just so there is no confusion here, does Sarah mean that she counts to infinity as opposed to counting towards infinity? There is a difference, and I feel like this is an important, but subtle, detail to address.
  $endgroup$
  – Mr Pie
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @MrPie All the way to infinity!
  $endgroup$
  – PerpetualJ
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  This question feels a bit too broad. Are you sure there's one demonstrably correct answer to this one?
  $endgroup$
  – PiIsNot3
  45 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @PiIsNot3 I’m pretty sure there is one way to count to the end of an infinite set in a finite time span.
  $endgroup$
  – PerpetualJ
  22 mins ago
  

  
  
  
  

 | 
show 1 more comment

$begingroup$

It’s been a while since my last post since school, work, and family have kept me incredibly busy. I have another puzzle though and as always I wish you the best of luck.

Sarah called me today and explained that she had counted to infinity. I shrugged and said it was impossible. She said that since I didn’t believe her, she would do it again, and this time in only ten minutes. I thought it was impossible but she did it right before my eyes!

How did Sarah count to infinity in only ten minutes?

Clarifications

Sarah indeed counted all the way to infinity.

riddle mathematics knowledge story

share|improve this question

edited 1 hour ago

PerpetualJ

asked 1 hour ago

PerpetualJPerpetualJ

4,130547

$endgroup$

share|improve this question

edited 1 hour ago

PerpetualJ

asked 1 hour ago

PerpetualJPerpetualJ

4,130547

share|improve this question

edited 1 hour ago

PerpetualJ

asked 1 hour ago

PerpetualJPerpetualJ

4,130547

asked 1 hour ago

PerpetualJPerpetualJ

4,130547

asked 1 hour ago

PerpetualJPerpetualJ

4,130547

3 Answers
3

active

oldest

votes

3

$begingroup$

Perhaps

clever Sarah went the appropriate "I" page in the dictionary and counted word entries until she reached "infinity"

share|improve this answer

answered 57 mins ago

SteveVSteveV

6,8832634

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If so, she didn't count to infinity, she (at best) counted to "infinity". (Personally I don't think even that is a correct description of what she did.) But I don't expect whatever answer OP has in mind to be much more convincing than this.
  $endgroup$
  – Gareth McCaughan♦
  15 mins ago
  

  
  
  
  

add a comment | 

1

$begingroup$

This feels underspecified:

clearly Sarah is not counting 1, 2, 3, ... (infinitely many numbers go here), infinity; so she's doing something else; but there are quite a lot of something-elses that she could do, and all of them are kinda cheaty, and the question here is what specific kinda-cheaty thing she did.

Here are a few possibilities. One:

She wrote numbers down on their sides, starting at 1 and proceeding as far as 8. An 8 on its side looks very much like the usual mathematical symbol for infinity.

Two:

She started from, let's say, "infinity minus 100" and counted up. (There are in fact number systems in which something a bit like "infinity minus 100" is an actual number.)

Three:

She counted down from, let's say, "infinity plus 100". (You can do something like that in the surreal numbers, mentioned above, but also in other simpler systems such as the ordinal numbers.)

Four:

She started counting normally, and at some point went "... and so on; infinity." I personally wouldn't (ahahaha) count that as counting to infinity, but then I don't think I'd count anything as counting to infinity other than the thing she obviously didn't do.

Five:

Sarah is able to count arbitrarily fast (maybe she's an archangel or something, not a human) and she said each number twice as quickly as its predecessor; after twice the time it took her to say "one", she had named all the positive integers and then said "infinity".

share|improve this answer

answered 1 hour ago

Gareth McCaughan♦Gareth McCaughan

68.9k3174270

$endgroup$

add a comment | 

0

$begingroup$

The definition of infinity in some circles is

the highest conceivable number.

Therefore, all Sarah needs to do is count to

the highest number she knows of, be that a hundred, a thousand, whatever. Because she cannot think of any number higher than that, that is her "infinity".

share|improve this answer

answered 1 hour ago

BewildererBewilderer

2645

$endgroup$

add a comment | 

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3

$begingroup$

Perhaps

clever Sarah went the appropriate "I" page in the dictionary and counted word entries until she reached "infinity"

share|improve this answer

answered 57 mins ago

SteveVSteveV

6,8832634

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If so, she didn't count to infinity, she (at best) counted to "infinity". (Personally I don't think even that is a correct description of what she did.) But I don't expect whatever answer OP has in mind to be much more convincing than this.
  $endgroup$
  – Gareth McCaughan♦
  15 mins ago
  

  
  
  
  

add a comment | 

3

$begingroup$

Perhaps

clever Sarah went the appropriate "I" page in the dictionary and counted word entries until she reached "infinity"

share|improve this answer

answered 57 mins ago

SteveVSteveV

6,8832634

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If so, she didn't count to infinity, she (at best) counted to "infinity". (Personally I don't think even that is a correct description of what she did.) But I don't expect whatever answer OP has in mind to be much more convincing than this.
  $endgroup$
  – Gareth McCaughan♦
  15 mins ago
  

  
  
  
  

add a comment | 

$begingroup$

Perhaps

clever Sarah went the appropriate "I" page in the dictionary and counted word entries until she reached "infinity"

share|improve this answer

answered 57 mins ago

SteveVSteveV

6,8832634

$endgroup$

share|improve this answer

answered 57 mins ago

SteveVSteveV

6,8832634

answered 57 mins ago

SteveVSteveV

6,8832634

answered 57 mins ago

SteveVSteveV

6,8832634

1

$begingroup$

This feels underspecified:

clearly Sarah is not counting 1, 2, 3, ... (infinitely many numbers go here), infinity; so she's doing something else; but there are quite a lot of something-elses that she could do, and all of them are kinda cheaty, and the question here is what specific kinda-cheaty thing she did.

Here are a few possibilities. One:

She wrote numbers down on their sides, starting at 1 and proceeding as far as 8. An 8 on its side looks very much like the usual mathematical symbol for infinity.

Two:

She started from, let's say, "infinity minus 100" and counted up. (There are in fact number systems in which something a bit like "infinity minus 100" is an actual number.)

Three:

She counted down from, let's say, "infinity plus 100". (You can do something like that in the surreal numbers, mentioned above, but also in other simpler systems such as the ordinal numbers.)

Four:

She started counting normally, and at some point went "... and so on; infinity." I personally wouldn't (ahahaha) count that as counting to infinity, but then I don't think I'd count anything as counting to infinity other than the thing she obviously didn't do.

Five:

Sarah is able to count arbitrarily fast (maybe she's an archangel or something, not a human) and she said each number twice as quickly as its predecessor; after twice the time it took her to say "one", she had named all the positive integers and then said "infinity".

share|improve this answer

answered 1 hour ago

Gareth McCaughan♦Gareth McCaughan

68.9k3174270

$endgroup$

add a comment | 

1

$begingroup$

This feels underspecified:

clearly Sarah is not counting 1, 2, 3, ... (infinitely many numbers go here), infinity; so she's doing something else; but there are quite a lot of something-elses that she could do, and all of them are kinda cheaty, and the question here is what specific kinda-cheaty thing she did.

Here are a few possibilities. One:

She wrote numbers down on their sides, starting at 1 and proceeding as far as 8. An 8 on its side looks very much like the usual mathematical symbol for infinity.

Two:

She started from, let's say, "infinity minus 100" and counted up. (There are in fact number systems in which something a bit like "infinity minus 100" is an actual number.)

Three:

She counted down from, let's say, "infinity plus 100". (You can do something like that in the surreal numbers, mentioned above, but also in other simpler systems such as the ordinal numbers.)

Four:

She started counting normally, and at some point went "... and so on; infinity." I personally wouldn't (ahahaha) count that as counting to infinity, but then I don't think I'd count anything as counting to infinity other than the thing she obviously didn't do.

Five:

Sarah is able to count arbitrarily fast (maybe she's an archangel or something, not a human) and she said each number twice as quickly as its predecessor; after twice the time it took her to say "one", she had named all the positive integers and then said "infinity".

share|improve this answer

answered 1 hour ago

Gareth McCaughan♦Gareth McCaughan

68.9k3174270

$endgroup$

add a comment | 

$begingroup$

This feels underspecified:

clearly Sarah is not counting 1, 2, 3, ... (infinitely many numbers go here), infinity; so she's doing something else; but there are quite a lot of something-elses that she could do, and all of them are kinda cheaty, and the question here is what specific kinda-cheaty thing she did.

Here are a few possibilities. One:

She wrote numbers down on their sides, starting at 1 and proceeding as far as 8. An 8 on its side looks very much like the usual mathematical symbol for infinity.

Two:

She started from, let's say, "infinity minus 100" and counted up. (There are in fact number systems in which something a bit like "infinity minus 100" is an actual number.)

Three:

She counted down from, let's say, "infinity plus 100". (You can do something like that in the surreal numbers, mentioned above, but also in other simpler systems such as the ordinal numbers.)

Four:

She started counting normally, and at some point went "... and so on; infinity." I personally wouldn't (ahahaha) count that as counting to infinity, but then I don't think I'd count anything as counting to infinity other than the thing she obviously didn't do.

Five:

Sarah is able to count arbitrarily fast (maybe she's an archangel or something, not a human) and she said each number twice as quickly as its predecessor; after twice the time it took her to say "one", she had named all the positive integers and then said "infinity".

share|improve this answer

answered 1 hour ago

Gareth McCaughan♦Gareth McCaughan

68.9k3174270

$endgroup$

share|improve this answer

answered 1 hour ago

Gareth McCaughan♦Gareth McCaughan

68.9k3174270

answered 1 hour ago

Gareth McCaughan♦Gareth McCaughan

68.9k3174270

answered 1 hour ago

Gareth McCaughan♦Gareth McCaughan

68.9k3174270

0

$begingroup$

The definition of infinity in some circles is

the highest conceivable number.

Therefore, all Sarah needs to do is count to

the highest number she knows of, be that a hundred, a thousand, whatever. Because she cannot think of any number higher than that, that is her "infinity".

share|improve this answer

answered 1 hour ago

BewildererBewilderer

2645

$endgroup$

add a comment | 

0

$begingroup$

The definition of infinity in some circles is

the highest conceivable number.

Therefore, all Sarah needs to do is count to

the highest number she knows of, be that a hundred, a thousand, whatever. Because she cannot think of any number higher than that, that is her "infinity".

share|improve this answer

answered 1 hour ago

BewildererBewilderer

2645

$endgroup$

add a comment | 

$begingroup$

The definition of infinity in some circles is

the highest conceivable number.

Therefore, all Sarah needs to do is count to

the highest number she knows of, be that a hundred, a thousand, whatever. Because she cannot think of any number higher than that, that is her "infinity".

share|improve this answer

answered 1 hour ago

BewildererBewilderer

2645

$endgroup$

share|improve this answer

answered 1 hour ago

BewildererBewilderer

2645

answered 1 hour ago

BewildererBewilderer

2645

answered 1 hour ago

BewildererBewilderer

2645