We can do with zero the same we can do with infinity.
lim [t → ∞] [f(t)/g(t)] = 0
f(t) = c, g(t) = at
f(t) = ctⁿ, g(t) = ktª, a > n
f(t) = ln t, g(t) = t
f(t) = ctⁿ, g(t) = t!
f(t) = t!, g(t) = t^t
lim [t → ∞] | g(t)/f(t) | = ∞
0 ⋅ ∞ = 0/0 = ∞ ⋅ ∞ are three indeterminations
1^∞ = exp(ln( 1^∞ )) = exp(∞ ln(1)) = exp(∞ ⋅ 0) is another indetermination
I'm worried with
cardinality (set A): # A < 0
norm (vector v): ||v|| < 0
inner product: <v, v> < 0
distance(vectors): dist(u, v) < 0
diameter(set A): diam A < 0
dimension(space U): dim U < 0
It seems to me that for those negativities exist, we need to invent some things out of standards.
Vinicius
twitter.com/mathspiritual
Em quarta-feira, 4 de janeiro de 2017 10:45:59 UTC-2, Charlie-Boo escreveu:
I am mostly interested in things you can and cannot do with zero. For example, you can divide both sides of an equation by the same number EXCEPT if it's zero. You can express A*B=0 as (A=0)v(B=0).