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It was a dark and stormy afternoon. The fog* was dense except during the stormer parts of the stormy weather (which were dark) during the stormy afternoon and night (which was dark and stormy).
* I know this is all different from the actual text of the dark and stormy night thing, but...
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ
Yesterday my seatmate was doing something with her green ballpen (she doesn't know why it happened and I wasn't looking) and it exploded. At first I thought someone threw green paint. It was on my index finger, my wrist, my uniform, my pants and some of my books, notebooks, and pad paper.
PkmnQ wrote:Yesterday my seatmate was doing something with her green ballpen (she doesn't know why it happened and I wasn't looking) and it exploded. At first I thought someone threw green paint. It was on my index finger, my wrist, my uniform, my pants and some of my books, notebooks, and pad paper.
I like green anyway.
"Green hair!" -- Rarity
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It looks like people have forgot about this rule, when I wrote:
Hunting wrote:I really want a OCA:SparseMethuseLife page for this rule, and LifeViewer Aliases, and other things when this rule is explored. I know the fact that this rule is not really interesting, since it's almost impossible to have a gun or rake or something like that and thus engineering is highly limited, but I believe it have potential too.
Define x as ∑(infinity)1.
x is effectively 1 * infinity, or infinity.
By definition, x-x = inf-inf = inf.
However, when collapsing the summation, we get ∑(infinity)(1-1) = 0.
testitemqlstudop wrote:Here's something to bend you minds:
Define x as ∑(infinity)1.
x is effectively 1 * infinity, or infinity.
By definition, x-x = inf-inf = inf.
However, when collapsing the summation, we get ∑(infinity)(1-1) = 0.
That only works if you have cardinals; w-w is not well defined in the simplest system involving transfinite ordinals, since you can’t subtract from limit ordinals.
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ
What are you even summing over in "Σ(inf)(1-x)"? I only understand it as "adding (1-x) infinite times", which would be identical to infinity.
However, the statement
lim(x->1)(Σ(inf)(1-x)) >> Σ(inf)(1-1)
is wrong, because you are defining Σ(inf)(1-1) as 0. The value of 0*inf is undefined. Proof: Suppose otherwise, that 0*inf = x. Hence, x/0 = inf, bu division by 0 is inherently undefined. (Don't even think about defining limits for x/0, that's not what I'm trying to get at here.)
What are you even summing over in "Σ(inf)(1-x)"? I only understand it as "adding (1-x) infinite times", which would be identical to infinity.
However, the statement
lim(x->1)(Σ(inf)(1-x)) >> Σ(inf)(1-1)
is wrong, because you are defining Σ(inf)(1-1) as 0. The value of 0*inf is undefined. Proof: Suppose otherwise, that 0*inf = x. Hence, x/0 = inf, but division by 0 is inherently undefined. (Don't even think about defining limits for x/0, that's not what I'm trying to get at here.)
So you can't compare anything to Σ(inf)0.
I’m sorry, but Σ(inf)0 =/= “your 0*inf” — it’s equal to 0+0+0+0+0+0+0+0+0+0+0+0+0+0... = 0.
While Σ(n)(k) = nk for finite, constant n and k, Σ(inf)0 =/= “0*inf”. You’re just adding 0 infinitely many times. While this IS mutiplication, it’s clear that 0+0+0+0+0+0+0+0+0+0+0+0+0=0ω. So maybe I should be more precise.
Σ(ω)(1-1) << lim(x->1)(Σ(ω)(1-x))
Basically, inf isn’t a number so of course 0*inf is undefined. In contrast, 0w is defined as 0.
Last edited by Moosey on June 25th, 2019, 2:18 pm, edited 1 time in total.
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ