• I asked God if he could buy me  a girl.He said no because they have infinite value.......And If he spent infinity dollars he would have nothing left to buy anything else.................That is the joke see what Nils does with it below

  
  

  Joe Blogs

  • So now my blog has been updated.............
  • Whenever anything new happens people always try to say it is nonsense because of X,Y,Z what is known is everything that is known.
  • I let Wolfram know that his engine does not work for 2 E=MC^2?
  • Maybe they will make it work.........and not just for the constant e which is of course a mistake.
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  a few seconds ago

  Nils Baeté

  • You can't use ∞ like you use ordinary numbers.
    ∞ and -∞ are not elements from R (real numbers).
    (In fact ∞ and -∞ are elements from the compactification of R, or also called the extended real numbers)
    
    As far as i know there are 2 different ways infinity can be used:
    1) Ordinal and cardinal infinities in set theory.
    2) Unbounded limit in analysis
    
    1)
    In the case of set theory you have for example the cardinality of a set (the size of the set, or in other words the amount of elements of the set).
    In case of infinite sets (sets with an infinite amount of elements) there are 2 different types of "infinity": countable infinity (the size of a countable infinite set), and uncountable infinity (the size of an uncountable set).
    
    A set is a countable infinite set if a bijection exists between that set and the natural numbers (N).
    Examples of countable infinite sets are: natural numbers (N), integers (Z) and rational numbers (Q).
    
    A set is an uncountable set if a bijection exists between that set and the real numbers (R).
    Examples of uncountable sets are: real numbers (R), trancedental numbers, the interval ]0, 1[ .
    
    Both types of infinite sets have an infinite size, but these two sizes are still very different from each other.
    It is possible to "count" the elements from a countable (infinite) set. But it is impossible to "count" the elements from an uncountable set.
    
    Examples for counting elements from countable (infinite) sets:
    N: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...
    Z: 0, 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, ...
    The elements from uncountable sets, like for example R, can't be counted. I mean ... how the hell would you count the real numbers?
    
    
    2)
    In the case of analysis you might encounter unbounded limits and these unbounded limits are denoted as +∞ and -∞ (instead of +∞ you can also write ∞ ofcourse)
    This can be the limit from something for a parameter going to ∞ . but it is also possible that the limit from something for a parameter going to a specific value is unbounded (this means that the limit itself equals ∞).
    
    This can be a limit from a function, a sequence, a (sum) series, product series or other series, an integral, a continued fraction, continued root, continued exponentiation, continued tetration, etc ...
• 

  a few seconds ago

  Nils Baeté

  • If you want to apply set theory to it then you have several difficulties, and with the few information we have we can't find out the result.
    
    Lets say god has an infinite set A that he can use (i dont know what it's elements are, was it money or something else?). And lets say he requires an infinite set B to "buy" you a girl.
    
    We don't know what cardinality A and B have. In other words what is the size of A and B? Just saying "infinite" is not enough info since it can either be countable or uncountable.
    
    If you make the difference of these two sets you still don't know what will be left behind with the very few info we have.
    
    In general it is mathematicall impossible to find out the size of the set C wich is the difference between the sets A and B, just by trying to take the difference between the sizes of sets A and B.
    
    The correct way to do it is to work with set theory, wich in this case doesn't requires the sizes of the sets.
    
    First of all is B even a subset of A? Because if it isn't then it's obvious that he can't "buy" you a girl.
    
    In the case B is a subset from A, then we still don't know anything.
    Lets say C = A\B
    (A\B is the relative complement of B in A, it is like "substracting" B from A)
    C=A\B=Ø if and only if A=B or A=Ø
    But since we know the cardinality of A is atleast countable infinite, this rules out A=Ø.
    ==> A=B
    
    It is not because A and B have both infinite cardinality that god can't buy you a girl, he can't because A equals B or because B isn't a subset from A. Cardinality (size from the sets) have nothing to do with this as you can see).
    
    To give other examples to show that the relative complement from a set B in a set A is not nessesarily 0 if both sets have the same cardinality:
    
    N is the set of the natural numbers, Z is the set of the integers.
    As you know N is a subset from Z, and both N and Z are countable infinite.
    Z\N = Zˉ\{0} ≠ Ø
    (where Zˉ\{0} are the negative integers except 0,
    and Zˉ\{0} is also countable infinite)
    
    R are the real numbers, and lets say I are the irrational numbers. I is a subset from R and both sets are uncountable.
    R\I = Q ≠ Ø
    (Q are the rational numbers, wich is countable infinite, thus cardinality changed!)
    
    Lets say A are the algebraic numbers (numbers that can be expressed as roots from non-zero polynomials in one variable with rational coefficients. For example: al rational numbers are algebraic numbers, all rational roots from rational numbers are algebraic numbers, ... . Numbers that are not algebraic are called "trancedental numbers".)
    A is a subset of R. R is uncountable while A is countable infinite.
    R\A = T ≠ Ø
    (Where T is the set of trancedental numbers (non-algebraic numbers). Examples of trancedental numbers are π and e. T is uncountable)
    
    R+ and R- are respectively the positive real numbers and negative real numbers.
    both R+ and R- are subsets from R, all of wich are uncountable.
    R\R+ = R-\{0} ≠ Ø
    
    
    If C=A\B <==> B=A\C
    
    In general there is no relation between the cardinality of A, B and C. But in specifical cases there is:
    
    Lets say B is a subset from A (and so C is also a subset from A since C=A\B):
    
    - If A and B are finite, then C will be finite too.
    
    - If A has an infinite cardinality (countable or uncountable) and B is finite, then C will have the same cardinality as A.
    
    - If A is uncountable and B is countable, then C will be uncountable.
    
    In all other case there is no rule, then it depends on the specific sets.
• 

  a few seconds ago

  Nils Baeté

  • In case you want to apply analysis:
    
    ∞ - ∞ is an undeterminacy wich depends on the limit of a function, sequence, series, ... .
    
    In general ∞ - ∞ can be any extended real number
    (R U {-∞, +∞})
    
    Example with functions:
    
    For example take the function f(x) = x² - x
    If you take the limit for x→∞ then you will get
    lim_(x→∞) (x² - x) = ∞ - ∞
    But since x² increases quadratic while x increases linear, the x² term will be dominant.
    So this means: lim_(x→∞) (x² - x) = ∞
    
    Another example is the function f(x) = x/(x-1) - 1/ln(x)
    If you take the limit for x→1 then you also get ∞ - ∞
    But after some conversions and applying L'Hôpital's rule you will find that this limit equals 1/2
    
    Another example is f(x) = sinh(x) - cosh(x)
    If you take the limit for x→∞ will wil get something of the form ∞ - ∞
    But after converting them into exp functions you will see that this limit equals 0
    
    So as you can see i already gave 3 situations in wich
    ∞ - ∞ has different solutions for each of the examples (∞, 1/2 and 0)
    ∞ - ∞ can be any element of R U {∞, -∞}, it all depends on the function or sequence or series or ... .