The lack of a solution to x = x + 1 is proof God doesn't exist

Because there's no way any sort of omnipotent being would be stupid enough to create a universe where numbers don't work to satisfy that equation. Obviously.
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  • Eternity is a child playing, playing checkers; the kingdom belongs to a child.
    I close my eyes and see a flock of birds. The vision lasts a second or perhaps less; I don’t know how many birds I saw. Were they a definite or an indefinite number? This problem involves the question of the existence of God. If God exists, the number is definite, because how many birds I saw is known to God. If God does not exist, the number is indefinite, because nobody was able to take count. In this case, I saw fewer than ten birds (let’s say) and more than one; but I did not see nine, eight, seven, six, five, four, three, or two birds. I saw a number between ten and one, but not nine, eight, seven, six, five, etc. That number, as a whole number, is inconceivable; ergo, God exists.

  • listen, it's not god's fault you're too boring to consider ∞ a number
  • edited 2017-11-07 01:39:35

    image
  • vtkvtk
    embrace the confusion
    I'm pretty sure there are some algebras in which there exists a value x such that x + 1 = x. But when I read Wikipedia articles on such concepts I don't really understand them.
  • kill living beings
    under the reals mod one x = 0.5 i guess?
  • edited 2017-11-07 16:14:51
    vtk said:

    I'm pretty sure there are some algebras in which there exists a value x such that x + 1 = x. But when I read Wikipedia articles on such concepts I don't really understand them.

    Depends on what you mean by "algebra". The main problem with infinity is that you can't really subtract infinity from things (that's basically taking the logarithm of division by zero), so you can't get a ring, but you can invent an algebraic structure that doesn't have subtraction, like a semiring, and then you're good. Or you can be an analyst who works with functions defined "almost everywhere", and then it's okay if subtraction sometimes doesn't work.

    under the reals mod one x = 0.5 i guess?

    That also works, for a slightly different interpretation than mine. (Though there's nothing special about 0.5; if you're working mod 1 then everything solves this equation!)
  • Hope will exist in a problematic relationship with reason
    Whenever u math people talk about math it makes me want to learn lots of math
  • Whenever u math people talk about math it makes me want to scream and jump off a cliff screaming
  • Whenever u math people talk about math u talk about math
  • Hope will exist in a problematic relationship with reason
    Imagine the alternative, you run up to the edge of the cliff screaming and are silent as you go over the edge
  • interesting
  • What if your scream volume is constant so long as you're above solid ground but then decays asymptotically when you're in mid-air?
  • want 2 be smugg? sip from the mugg
    if Imipolex jumps off a cliff at 8,000 feet up, and screams the entire way down, his volume decreasing by .5 decibels per minute, when does he hit the ground?
  • BeeBee
    edited 2017-11-07 17:21:08
    edit: whoops, nope
  • using + for logical OR is bad imo
  • Well Bee blanked his post, but it is true that if you do boolean logic using the engineer's convention that + means OR (and 1 means true), 1 is a solution.
  • image Wee yea erra chs hymmnos mea.
    Jane said:

    if Imipolex jumps off a cliff at 8,000 feet up, and screams the entire way down, his volume decreasing by .5 decibels per minute, when does he hit the ground?

    41:37 AM exactly.
  • edited 2017-11-07 18:20:10
    Sup bitches, witches, Haters, and trolls.

    using + for logical OR is bad imo

    the correct symbol for logical or is ∨
  • Sup bitches, witches, Haters, and trolls.
    wtf it works in preview but not in the actual post
  • Calica said:

    using + for logical OR is bad imo

    the correct symbol for logical or is ∨
    yes
  • Calica said:

    wtf it works in preview but not in the actual post

    and it even works in my quote! vanilla is truly amazing software
  • Sup bitches, witches, Haters, and trolls.
    okay using "or" instead of "vee" worked.
  • Sup bitches, witches, Haters, and trolls.
    it works in your quote because i changed it to or instead of vee after you quoted.

    but it's also the correct symbol for "max" so it's not just or and that's why you should use abstract names for the symbol
  • kill living beings

    under the reals mod one x = 0.5 i guess?

    That also works, for a slightly different interpretation than mine. (Though there's nothing special about 0.5; if you're working mod 1 then everything solves this equation!)
    furious blush here
    Jane said:

    if Imipolex jumps off a cliff at 8,000 feet up, and screams the entire way down, his volume decreasing by .5 decibels per minute, when does he hit the ground?

    dB is a log scale so he just screams forever. presumably he's held up by some kind of geyser or space monster
  • lucky me
  • using + for logical OR is bad imo


    It's useful for distributive purposes.

    Yeah on second thought I didn't need to blank that post because it was correct.
  • Bee said:

    using + for logical OR is bad imo


    It's useful for distributive purposes.

    Yeah on second thought I didn't need to blank that post because it was correct.
    Well sure, but in boolean logic you also have that OR distributes over AND, which is pretty weird if you think of them as addition and multiplication.

    Also, boolean logic is isomorphic to arithmetic modulo 2, but it's XOR that corresponds to addition. I think that's the main reason it bothers me.

    Though I guess now that I think about it, boolean OR and AND are the addition and multiplication of a semiring, so I can't really say it's any less of an example than the one(s) I was thinking of with infinities.
  • vtkvtk
    embrace the confusion
    Calica said:

    it works in your quote because i changed it to or instead of vee after you quoted.


    but it's also the correct symbol for "max" so it's not just or and that's why you should use abstract names for the symbol
    But if True > False, then "or" and "max" are practically equivalent on Boolean values.
  • vtkvtk
    embrace the confusion
    Centie hasn't even replied once in this thread
  • “And above all, watch with glittering eyes the whole world around you because the greatest secrets are always hidden in the most unlikely places. Those who don't believe in magic will never find it.” – Roald Dahl
    I can't think of anything to say, mostly because I don't actually understand any of the math y'all are talking about
  • kill living beings
    You know what the number line is, right? You add one, you move one spot to the right on the line.

    Doing arithmetic "mod whatever" means you take a line segment of length whatever, cut it out of the line, and tie the ends together so it makes a loop. So if you have 7 + 2 mod 8, you start seven over from zero, then move two to the right. You cross zero so you end up one to the right of zero, so the answer is 1.

    mod 1 just means the loop is of length 1, so adding 1 is just going all the way around the loop once. So any number equals one plus itself in that system.
  • “And above all, watch with glittering eyes the whole world around you because the greatest secrets are always hidden in the most unlikely places. Those who don't believe in magic will never find it.” – Roald Dahl
    That makes sense.
  • Hope will exist in a problematic relationship with reason

    You know what the number line is, right? You add one, you move one spot to the right on the line.


    Doing arithmetic "mod whatever" means you take a line segment of length whatever, cut it out of the line, and tie the ends together so it makes a loop. So if you have 7 + 2 mod 8, you start seven over from zero, then move two to the right. You cross zero so you end up one to the right of zero, so the answer is 1.
    I'm curious, what one does with this
  • edited 2017-11-08 15:12:29
    kill living beings
    Well usually you do it with integers rather than reals, so the width has to be greater than one to be interesting.

    The most practical application is what's called modular exponentiation. Basically just regular exponentiation ("to the power of") but mod whatever. Like for example, 2^6 mod 7 = 64 mod 7 = 1. Fairly straightforward.

    The convenient part is that it's really hard to get logarithms, i.e. to reverse the operation. Like, if you're just given 1, and told 2 to the power of something is 1 mod 7, it's hard to tell what the something is short of brute force, even though computing the forward operation was really easy.

    This makes it useful as a "trapdoor" function that's easy to do one way but hard to reverse, which is a backbone of cryptography.

    that's only one thing though. it's important for math proper as well. gauss did all kinds of shit with it
  • Hope will exist in a problematic relationship with reason
    Oooohhhh!!!!! That's really cool!!!!
  • edited 2017-11-08 15:29:11

    I can't think of anything to say, mostly because I don't actually understand any of the math y'all are talking about

    For what I was saying it mostly boils down to the fact that if you subtract x from both sides of that equation you get 0 = 1, so to have a solution you need to address that. Klino addressed it by just saying sure, 0 = 1, whereas I (and Bee) did it by moving to a land without subtraction.

    A "ring" is something where you can add, subtract, and multiply, eg. the integers. (If you can also divide, it's a "field".) A "semiring" is where you can add and multiply but not necessarily subtract, such as the nonnegative integers, or the integers with infinity thrown in.
  • kill living beings
    There's also the chinese remainder theorem: If you have a set of numbers "ni" that are pairwise coprime, i.e. no two of them share divisors, then you can uniquely determine any number mod N by what it is mod those ni, where N is the product of the ni.

    Which I'm sure makes no sense, so for example, say n1 = 2, n2 = 3, n3 = 5. N = n1*n2*n3 = 30. If we pick a number, let's say 13, we can compute 13 mod n1 = 1, 13 mod n2 = 1, and 13 mod n3 = 3. No other number from zero to 29 shares that (1, 1, 5) set.

    As a bonus, we can compute with those. To take 13 + 13 we can take 1 + 1 mod n1 = 0, 1 + 1 mod n2 = 2, 3 + 3 mod n3 = 1. And hey, 26 mod n1 = 0, 26 mod n2 = 2, 26 mod 5 = 1, it works.

    You can use this to represent really large numbers conveniently. Like, 5829472801, that's pretty big, right? Too big to fit in 32 bits of computer memory for example. But the product of the first eleven primes is bigger, so we can just take x = 5829472801, and then x mod 2 = 1, etc., and we can represent it as (1, 1, 1, 5, 9, 9, 13, 18, 4, 14), all pretty small.
  • Eternity is a child playing, playing checkers; the kingdom belongs to a child.
    pf nerds
  • Hope will exist in a problematic relationship with reason
    This all makes me really wanna study math ;w;
  • Tamlin said:

    This all makes me really wanna study math ;w;

    nobody's stopping you~
  • Eternity is a child playing, playing checkers; the kingdom belongs to a child.

    Tamlin said:

    This all makes me really wanna study math ;w;

    nobody's stopping you~
    *cocks shotgun*
  • want 2 be smugg? sip from the mugg
    *emerges from the bushes with a knife*
  • That makes sense.

    FYI they actually call mod arithmetic "clock arithmetic" because that's basically how clocks work.
  • edited 2017-11-08 17:49:07


    That makes sense.

    FYI they actually call mod arithmetic "clock arithmetic" because that's basically how clocks work.
    Eh, the clock thing is a common way to teach it but it's not actually a fantastic analogy. You don't take 5 o'clock and add 8 o'clock to get 1 o'clock, that doesn't make sense. You take 5 o'clock and add eight hours to get 1 o'clock. Times are different from time intervals; to use fancy words, a clock is actually a torsor for the additive group mod 12, rather than being the group itself.

    That's not even to get into the fact that modular multiplication doesn't mean anything for clocks.
  • kill living beings
    i'm imagining this in terms of ptrdiff_t even though i understand voltage perfectly well aaaaah
  • I am still screaming
  • BeeBee
    edited 2017-11-08 20:01:37
    I don't think I've ever run into a situation where full-on persistent modulus algebra is useful, but we use mod functions in programming all the time because integer remainders are important to a lot of things.  The main one is to take Unix-time measurements (milliseconds) and convert them piece by piece into hours/minutes/seconds, today's date-time, weeks + days, etc.  The operator is a %, e.g., 15 % 4 = 3.

    In some of the lower-level bit ops, you can perform quick power-of-two integer-divs and mods by just bit shifting until all the upper/lower bits vanish and you're left with whatever.  This is pretty common in older games where computation was at a premium and they made sure to subdivide everything they could by some power of two specifically to be able to leverage bit ops like this.
  • Sup bitches, witches, Haters, and trolls.
    another torsor: the 3x3x3 rubik's cube (but not bigger ones; "not a group" is better described as "not a torsor")
  • vtkvtk
    edited 2017-11-08 21:45:24
    embrace the confusion


    A "ring" is something where you can add, subtract, and multiply,

    Ooh I have a favorite one of those. It's like a complex version of the numbers with a terminating phinary expression and it has a one-to-one mapping to Z4. I've kind of invented it myself, so I haven't completely settled on the notation yet, though it's possible someone else has already worked with this ring.

    Okay, might as well try a notation here. If we write a number as Sk + Ri + Nj + M, where M, N, R, S are integers and i, j, k are constants, there are several identities to define.
    j² = j + 1. (j is the golden ratio.)
    ij = ji = k.
    i² = k - i - 1.
    ik = ki = ji² = k - j - 1.
    jk = kj = k + i.
    i³ = -k + i - j + 1.
    i4 = -i + j - 1.
    k² = k - j - 1.
    i5 = 1.
    (k - i + j - 1)² = i.
    Have I missed anything?
  • vtkvtk
    embrace the confusion
    Also, division by i and division by j are possible, but only because i · (-i + j - 1) = 1 and j · (j - 1) = 1. Division by arbitrary numbers isn't really a thing.
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