User:Objectz/Math

This is my math subpage. These contain functions that I have created.

$x \downarrow y = x^{-(x \uparrow y)}$ where $x \uparrow y = x^{y}$ so $3 \downarrow 3 = 3^{-(3 \uparrow 3)} = 3^{-27}$ .

$x \downarrow \downarrow y = (x \uparrow y)^{-(x \uparrow y)}$ so $3 \downarrow \downarrow 3 = (3 \uparrow 3)^{-(3 \uparrow 3)} = 27^{-27} = 3^{-81}$ .

$x \downarrow \downarrow \downarrow y = (x \uparrow \uparrow y)^{-(x \uparrow y)}$ . So, $3 \downarrow \downarrow \downarrow 3 = (3 \uparrow \uparrow 3)^{-(3 \uparrow 3)} = 7625597484987^{-27} = 3^{-729}$ .

$x \downarrow \downarrow \downarrow \downarrow y = (x \uparrow \uparrow \uparrow y)^{-(x \uparrow y)}$ . So, $3 \downarrow \downarrow \downarrow \downarrow 3 = (3 \uparrow \uparrow \uparrow 3)^{-(3 \uparrow 3)} = (3^{7625597484987})^{-27} = 3^{-205891132094649}$ .

$10 \downarrow \downarrow \downarrow \downarrow 10 = (10 \uparrow \uparrow \uparrow 10)^{-(10 \uparrow 10)} = (10 \uparrow \uparrow \uparrow 10)^{-10000000000} = \boxed{(10^{10^{10000000000}})^{-10000000000}}$ .

$10 \underbrace{\downarrow \downarrow \downarrow \downarrow \downarrow \downarrow \cdots \downarrow \downarrow \downarrow \downarrow \downarrow \downarrow}_{10 \downarrow \downarrow \downarrow \downarrow 10} 10 = ObjectZ_{1}$ .

$10 \underbrace{\downarrow \downarrow \downarrow\downarrow \downarrow \downarrow \downarrow \downarrow \downarrow \cdots \downarrow \downarrow \downarrow \downarrow \downarrow \downarrow \downarrow \downarrow \downarrow}_{10 \underbrace{\downarrow \downarrow \downarrow \downarrow \downarrow \downarrow \cdots \downarrow \downarrow \downarrow \downarrow \downarrow \downarrow}_{10 \downarrow \downarrow \downarrow \downarrow 10} 10} 10 = ObjectZ_{2}$ .

$ObjectZ_{513298}$ is ObjectZ's Number.

$n_{\Omega}(1) = \underbrace{ObjectZ_{ObjectZ_{ObjectZ_{ObjectZ_{ObjectZ_{ObjectZ_{... _ {ObjectZ_{ObjectZ's ~ Number}}}}}}}}}_{ObjectZ's ~ Number}$ .

$n_{\Omega}(2)$ is the attachment in the post when you click on the link. https://artofproblemsolving.com/community/c1230676h2319478p18794259.

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User:Objectz/Math