# Math question **URL:** \ **Category:** Factual Questions\ **Created:** [September 6, 2010, 7:50pm UTC](https://boards.straightdope.com/t/math-question/552832 "2010-09-06T19:50:04Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![copperwindow](https://avatars.discourse-cdn.com/v4/letter/c/4af34b/32.png) [@copperwindow](https://boards.straightdope.com/u/copperwindow)\ **Post date:** [September 6, 2010, 7:50pm UTC](https://boards.straightdope.com/t/math-question/552832/1 "2010-09-06T19:50:04Z")
Is it correct to say that there are more numbers than english letters? ---
**Author:** ![Inner\_Stickler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/inner_stickler/32/318_2.png) [@Inner\_Stickler](https://boards.straightdope.com/u/Inner_Stickler)\ **Post date:** [September 6, 2010, 7:52pm UTC](https://boards.straightdope.com/t/math-question/552832/2 "2010-09-06T19:52:59Z")
Given that numbers are generally regarded as infinite in length and letters in the english alphabet pretty much peter out at 26, I’d say, yes. ---
**Author:** ![copperwindow](https://avatars.discourse-cdn.com/v4/letter/c/4af34b/32.png) [@copperwindow](https://boards.straightdope.com/u/copperwindow)\ **Post date:** [September 6, 2010, 7:56pm UTC](https://boards.straightdope.com/t/math-question/552832/3 "2010-09-06T19:56:11Z")
Infinity minus 26 is not infinity, it’s undifined. ---
**Author:** ![RadicalPi](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/radicalpi/32/9806_2.png) [@RadicalPi](https://boards.straightdope.com/u/RadicalPi)\ **Post date:** [September 6, 2010, 7:57pm UTC](https://boards.straightdope.com/t/math-question/552832/4 "2010-09-06T19:57:49Z")
It depends. If you’re considering the number of symbols, a first approach would be to compare 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 to a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, and z, and conclude there are more English letters. However, a number is generally considered to be distinct from the symbols used to write it, and so then, one can conclude that there are more numbers. Even if you disagree with this assessment, there are many numbers that are written without digits, π, φ, e (the number), that almost certainly bring the total to over 26, or even 52 if you decide that capitals are distinct. ---
**Author:** ![Inner\_Stickler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/inner_stickler/32/318_2.png) [@Inner\_Stickler](https://boards.straightdope.com/u/Inner_Stickler)\ **Post date:** [September 6, 2010, 7:57pm UTC](https://boards.straightdope.com/t/math-question/552832/5 "2010-09-06T19:57:56Z")
Why are you trying to subtract 26 from infinity? ---
**Author:** ![John\_Mace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/john_mace/32/185_2.png) [@John\_Mace](https://boards.straightdope.com/u/John_Mace)\ **Post date:** [September 6, 2010, 7:58pm UTC](https://boards.straightdope.com/t/math-question/552832/6 "2010-09-06T19:58:01Z")
The OP doesn’t make any sense. I think something is missing. Even if I replace “letters” with “words”, it still doesn’t make any sense: If the number of English words is x, then there exists a number, X+1. ---
**Author:** ![copperwindow](https://avatars.discourse-cdn.com/v4/letter/c/4af34b/32.png) [@copperwindow](https://boards.straightdope.com/u/copperwindow)\ **Post date:** [September 6, 2010, 8:03pm UTC](https://boards.straightdope.com/t/math-question/552832/7 "2010-09-06T20:03:03Z")
How can x+1 be more then x when x+1 is undefined? ---
**Author:** ![copperwindow](https://avatars.discourse-cdn.com/v4/letter/c/4af34b/32.png) [@copperwindow](https://boards.straightdope.com/u/copperwindow)\ **Post date:** [September 6, 2010, 8:06pm UTC](https://boards.straightdope.com/t/math-question/552832/8 "2010-09-06T20:06:11Z")
I’m talking about all real numbers.by the way, not symbols. ---
**Author:** ![Joey\_P](https://avatars.discourse-cdn.com/v4/letter/j/919ad9/32.png) [@Joey\_P](https://boards.straightdope.com/u/Joey_P)\ **Post date:** [September 6, 2010, 8:06pm UTC](https://boards.straightdope.com/t/math-question/552832/9 "2010-09-06T20:06:26Z")
> [@RadicalPi](#): > > It depends. > > If you’re considering the number of symbols, a first approach would be to compare 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 to a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, and z, and conclude there are more English letters. However, a number is generally considered to be distinct from the symbols used to write it, and so then, one can conclude that there are more numbers. Even if you disagree with this assessment, there are many numbers that are written without digits, π, φ, e (the number), that almost certainly bring the total to over 26, or even 52 if you decide that capitals are distinct. Those are digits and not just digits, but those are base 10 digits. The OP asked about numbers. > [@copperwindow](#): > > How can x+1 be more then x when x+1 is undefined? What does that have to do with anything…oh, wait, I think you have it backwards, look at it this way. There are 26 English Letters, I can very easily give you 27 numbers, therefore there are more numbers then English letters. Infinity doesn’t need to play in to this proof. ---
**Author:** ![Inner\_Stickler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/inner_stickler/32/318_2.png) [@Inner\_Stickler](https://boards.straightdope.com/u/Inner_Stickler)\ **Post date:** [September 6, 2010, 8:07pm UTC](https://boards.straightdope.com/t/math-question/552832/10 "2010-09-06T20:07:15Z")
Ok, i should have known better than to try to answer a copperwindow question. ---
**Author:** ![John\_Mace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/john_mace/32/185_2.png) [@John\_Mace](https://boards.straightdope.com/u/John_Mace)\ **Post date:** [September 6, 2010, 8:18pm UTC](https://boards.straightdope.com/t/math-question/552832/11 "2010-09-06T20:18:14Z")
> [@copperwindow](#): > > How can x+1 be more then x when x+1 is undefined? Why is it undefined? How are you defining “numbers” and “English letters”? This forum is called General Questions, btw, not General Riddles. ---
**Author:** ![Smeghead](https://avatars.discourse-cdn.com/v4/letter/s/f1d935/32.png) [@Smeghead](https://boards.straightdope.com/u/Smeghead)\ **Post date:** [September 6, 2010, 8:32pm UTC](https://boards.straightdope.com/t/math-question/552832/12 "2010-09-06T20:32:35Z")
Let’s start with the basics. Are you disputing the idea that infinity is larger than 26? ---
**Author:** ![DanBlather](https://avatars.discourse-cdn.com/v4/letter/d/f4b2a3/32.png) [@DanBlather](https://boards.straightdope.com/u/DanBlather)\ **Post date:** [September 6, 2010, 8:46pm UTC](https://boards.straightdope.com/t/math-question/552832/13 "2010-09-06T20:46:07Z")
No it is not correct, because in England people send letters all the time. Assuming that even one person sends one letter in his lifetime, and that England will always be with us, both numbers and English letters are infinite and therefore equal. ETA: I feel dirty ---
**Author:** ![74westy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/74westy/32/3950_2.png) [@74westy](https://boards.straightdope.com/u/74westy)\ **Post date:** [September 6, 2010, 9:13pm UTC](https://boards.straightdope.com/t/math-question/552832/14 "2010-09-06T21:13:14Z")
> [@DanBlather](#): > > No it is not correct, because in England people send letters all the time. Assuming that even one person sends one letter in his lifetime, and that England will always be with us, both numbers and English letters are infinite and therefore equal. You’re forgetting that the number of English letters, while infinite as you’ve shown, is discrete but copperwinwdow specified real numbers. > [@copperwindow](#): > > I’m talking about all real numbers.by the way, not symbols. Therefore there are more numbers than English letters. > [@DanBlather](#): > > ETA: I feel dirty Me too! ---
**Author:** ![President\_Johnny\_Gentle](https://avatars.discourse-cdn.com/v4/letter/p/5f9b8f/32.png) [@President\_Johnny\_Gentle](https://boards.straightdope.com/u/President_Johnny_Gentle)\ **Post date:** [September 6, 2010, 9:16pm UTC](https://boards.straightdope.com/t/math-question/552832/15 "2010-09-06T21:16:19Z")
> [@copperwindow](#): > > I’m talking about all real numbers.by the way, not symbols. Which means even if you’re comparing numbers to English words, there are more real numbers than words. ---
**Author:** ![Ace309](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ace309/32/1050_2.png) [@Ace309](https://boards.straightdope.com/u/Ace309)\ **Post date:** [September 6, 2010, 9:23pm UTC](https://boards.straightdope.com/t/math-question/552832/16 "2010-09-06T21:23:08Z")
> [@copperwindow](#): > > Infinity minus 26 is not infinity, it’s undifined. The limit of the function f(x) = x - 26 as x approaches infinity is infinity; would you at least agree with that? ---
**Author:** ![panache45](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/panache45/32/64_2.png) [@panache45](https://boards.straightdope.com/u/panache45)\ **Post date:** [September 6, 2010, 9:27pm UTC](https://boards.straightdope.com/t/math-question/552832/17 "2010-09-06T21:27:51Z")
How can something be undefined, when everyone knows what it means? ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 6, 2010, 9:41pm UTC](https://boards.straightdope.com/t/math-question/552832/18 "2010-09-06T21:41:56Z")
Infinity - 26 is perfectly well defined, within such systems as care to, you know, define it. E.g., the [affinely](http://en.wikipedia.org/wiki/Extended_real_number_line) or [projectively](http://en.wikipedia.org/wiki/Real_projective_line) extended number lines. But nevermind that. Is it correct to say there are more numbers than English letters? Taking the numbers to be the real numbers (this is a (purely historical and terribly misnamed) technical term, let us note; it does not mean “the numbers which are genuine” or any such thing) as requested, and the English letters to be the 26 familiar ones, then, yes, certainly, most mathematicians would speak that way. As **Joey P** said above, they would speak that way for reasons which needn’t have anything to do with infinities, even: among the real numbers, there are 27 integers from 0 through 26, inclusive, and thus more of these than there are English letters, in an extremely natural and obvious sense. Mind you, there are other senses in which one might care to speak of what “more” means, not all of which would justify the claim that there are more real numbers than English letters, but this particular sense seems the most pertinent to the OP’s question (though what the OP is after is actually quite unclear). ---
**Author:** ![digs](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/digs/32/14889_2.png) [@digs](https://boards.straightdope.com/u/digs)\ **Post date:** [September 6, 2010, 9:50pm UTC](https://boards.straightdope.com/t/math-question/552832/19 "2010-09-06T21:50:03Z")
OK, _ **THIS** _ is why some of us think common sense is pitched out the window when you get too much Math in your brain… Uh, just to double-check my common-sense answer, I counted to 27 in my head… to make sure. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 6, 2010, 9:51pm UTC](https://boards.straightdope.com/t/math-question/552832/20 "2010-09-06T21:51:11Z")
Who has too much math in their brain? Our OP appears to have extraordinarily, anomalously little… [Next page](https://boards.straightdope.com/t/math-question/552832.md?page=2)