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This is a very entertaining forum. I shall now algebraically count to infinity.
t= 1, 2, 3.....
n= 25, 26, 27.....
Therefore, the solution to the counting game (from this point onwards, i.e. '25' onwards) is:
n = t+24
The solution to this particular counting game (from the very beginning, i.e. '1') is:
n = t
With this algebraic formula, i have represented every number possible in the sequence, thus ending (and winning) this counting game --- is there a prize?
This is a very entertaining forum. I shall now algebraically count to infinity.
t= 1, 2, 3.....
n= 25, 26, 27.....
Therefore, the solution to the counting game (from this point onwards, i.e. '25' onwards) is:
n = t+24
The solution to this particular counting game (from the very beginning, i.e. '1') is:
n = t
With this algebraic formula, i have represented every number possible in the sequence, thus ending (and winning) this counting game --- is there a prize?
Sorry, becaude, for example, my last post, is 320-330 and this can be a random combination per post (n) therefore it must be n=RAN#+t
Also, Your algebraic function needs to change with each number, this works every time, it is the theory of Infinity (AQA Further Maths )
In theory the game is first x integers.
1, 2, 3, 4, 5, 6, 7, ... is the sequence of counting numbers. Each item in the list is its place number in the list.
Any set which can be put into one-one correspondence with N is called countable
Equations such as 1/infinity = 0 are not equations in the real number
(or complex number) system. They are shorthand for some equations
involving limits. The "infinity" in the above expression is short for:
lim g(x)
x->infinity where g(x) is any function which grows without bound as x does. In this
case, the equation is shorthand for:
This limit also uses the symbol infinity, but the limit has a precise
definition:
lim f(x) = L
x->infinity
is defined to mean that for any e > 0, no matter how small, there
exists a B (depending on e and f), such that for all x > B,
|f(x)-L| < e. In other words, as x grows without bound, f(x) gets
arbitrarily close to L.
Equations involving limits are, indeed, provable (or disprovable),
and so the shorthand versions are provable (or disprovable).
infinity - infinity = lim (x+c) - lim x = lim (x+c-x) = lim c = c
where c is any real number, and the limits are taken as x->infinity, or
write:
infinity - infinity = lim (2*x) - lim x = lim (2*x-x) = lim x
= infinity
Infinity is not a meaningful shorthand for
any limited equation, since it has no particular fixed values. Such
expressions is called an "indeterminate" expression, because you cannot
determine their values.
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