Question: How many sentences are possible in the English language? The answer doesn't have to be an exact amount, but I'd like to see a thought process for how someone would figure this out. Is the upper bound infinite?
I'm not a math major, so I'm stumped on this one.
with semicolons the sky is the limit, baby
With an ever changing language base, it's infinite.
what if there was a restriction that a sentence can be no longer than 100 words in length?
bguyj200012z2 wrote:
what if there was a restriction that a sentence can be no longer than 100 words in length?
Any restriction on technical words? "I'm sorry sir - I'm afraid you have pseudopseudohypoparathyroidism."
Maybe a more interesting question would be what's the longest sentence someone could make without using a comma, colon or semicolon?
Otherwise, one could consider sentences like: "The list of all possible lists of english words is as follows "apple","apple,aardvark","apple,aardvark,apple"..."
It should be pretty clear that there are an infinite number of sentences of that form.
If we go with the exclusion I put above then we would get sentences of the form
(+)
With modifiers, I could see the standard sentence being as many as 20 words long.
Let's say that there are 100,000 english words.
(10^5)^20=10^100 sentences. This is probably an overestimation though as you can't use every word as every part of speech. Assuming that each spot only has about 20% of all words available to it, then you get
(2*10^4)^20=~10^86 sentences.
combinatoric bs. here you go:
http://www.mathsisfun.com/combinatorics/combinations-permutations.html
split verbs from nouns from other, estimate the number of each in english, add names, adjust the combinatoric function for # words in the sentence. add b s.
"How many sentences are possible" is a sentence.
""How many sentences are possible"is a sentence" is a sentence.
"""How many sentences are possible" is a sentence" is a sentence" is a sentence.
and so on
don't need many words to realize the infinite
Goedel Goedel wrote:
"How many sentences are possible" is a sentence.
""How many sentences are possible"is a sentence" is a sentence.
"""How many sentences are possible" is a sentence" is a sentence" is a sentence.
and so on
don't need many words to realize the infinite
That's the right answer.
A more intuitive way to show it might be:
"One plus one is two. One plus two is three. One plus three is four . . ."
webby wrote:
Goedel Goedel wrote:"How many sentences are possible" is a sentence.
""How many sentences are possible"is a sentence" is a sentence.
"""How many sentences are possible" is a sentence" is a sentence" is a sentence.
and so on
don't need many words to realize the infinite
That's the right answer.
A more intuitive way to show it might be:
"One plus one is two. One plus two is three. One plus three is four . . ."
But in that case, won't you run out of words to describe the numbers?
webby wrote:
That's the right answer.
A more intuitive way to show it might be:
"One plus one is two. One plus two is three. One plus three is four . . ."
It is NOT infinite with the condition that bguyj added that sentences must be of length 100 words or less. As someone else pointed out above the number of possible sentences is then bounded by (W+1)^100 where W is the number of words in the English language. This is a fairly loose bound, but finite nonetheless.
Nope Nope wrote:
webby wrote:That's the right answer.
A more intuitive way to show it might be:
"One plus one is two. One plus two is three. One plus three is four . . ."
It is NOT infinite with the condition that bguyj added that sentences must be of length 100 words or less. As someone else pointed out above the number of possible sentences is then bounded by (W+1)^100 where W is the number of words in the English language. This is a fairly loose bound, but finite nonetheless.
Each of those sentences only has 5 words, so it fits the 100 word criteria.
Sentences can have numerals in them.
"After 1,234,567,890,123,456,789,012 comes 1,234,567,890,123,456,789,013. After that comes 1,234,567,890,123,456,789,014 . . ."
No Way wrote:
Nope Nope wrote:It is NOT infinite with the condition that bguyj added that sentences must be of length 100 words or less. As someone else pointed out above the number of possible sentences is then bounded by (W+1)^100 where W is the number of words in the English language. This is a fairly loose bound, but finite nonetheless.
Each of those sentences only has 5 words, so it fits the 100 word criteria.
Not exactly.
You have made two errors:
(1) Those sentences would not have only five words as you continued the sequence (one plus four hundred twenty one is four hundred twenty two...)
(2) There are not infinitely many words to describe numbers
As such, the fact remains that an upper bound is (W+1)^100. Limiting ourselves to sentences of 100 words or less certainly results in a finite limit. There is no getting around this.
There are an infinite number of possible sentences.
"1 is a number."
"2 is a number."
"3 is a number."
Just keep going with that. You do have the (W+1)^100 upper bound, but numbers are words, and there there are and infinite number of numbers, so W is infinity.
infinity wrote:
There are an infinite number of possible sentences.
"1 is a number."
"2 is a number."
"3 is a number."
Just keep going with that. You do have the (W+1)^100 upper bound, but numbers are words, and there there are and infinite number of numbers, so W is infinity.
Actually, numbers are not words. Numbers are mathematical objects. We use words to represent them. We also use numerals to provide a shorthand representation of the words. For example, "one" is the word that names the number which is also symbolized using the numeral "1".
Further, when used in a sentence, the numerals are actually just a shorthand way of representing the words. The actual sentence is as one would speak it, with the written shorthand being a convenient representation of the same thing. But the sentence contains the actual words.
Try saying "87,364 is a number". Spoken, this is "Eighty-seven thousand three hundred sixty-four is a number". As such, it is an eight word sentence (with two hyphenated words) and not a four word sentence.
W is not infinite and neither is the number of sentences of length less than or equal to 100 words.
"Runner one never gets laid because he is a dork who thinks about math problems all day."
"Runner two never gets laid because he is a dork who thinks about math problems all day."
Runner three never gets laid because he is a dork who thinks about math problems all day."
...
...
...
runners are dorks wrote:
"Runner one never gets laid because he is a dork who thinks about math problems all day."
"Runner two never gets laid because he is a dork who thinks about math problems all day."
Runner three never gets laid because he is a dork who thinks about math problems all day."
...
...
...
Actually, people whose intellectual capacity is stunted and cannot keep up resort to childish name calling using such clever words as "dork", "nerd"... This helps them feel better about themselves. The truth is that really smart guys get laid WAY more than your average Joe Sixpack who goes around calling people dorks whenever he cannot keep up.