Proof of Limit of Subfactorial

[iron sentinel]

I have to prove that limit if it's true or false, i believe it's true but not sure, please help

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[iron sentinel]

if you know what subfactorial is you can skip first image

[leaden pecan]

damn this is beautiful

[iron sentinel]

so, no one knows?

[flat pulsar]

(xy)²=(yz)²=(xz)²=xyyzxz=-1

[leaden pecan]

when x is approach ∞
the floor function ≈ the actual value

the difference of them is insignificant

[flat pulsar]

(xy)²=(yz)²=(xz)²=xyyzxz=-1

[leaden pecan]

then factor x! out then change its from a little

[leaden pecan]

sorry i put the sign wrong it's supposed to be +e^(-1)

[flat pulsar]

(xy)²=(yz)²=(xz)²=xyyzxz=-1

[leaden pecan]

@iron sentinel

[iron sentinel]

uuh there's floor function

[leaden pecan]

@iron sentinel

[iron sentinel]

the thing is we aren't able to use infinity in factorials