The Increasing Alphabet Number

The Increasing Alphabet Number is equal to Z↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑Y↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑X↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑W↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑V↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑U↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑T↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑S↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑R↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑Q↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑P↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑O↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑N↑↑↑↑↑↑↑↑↑↑↑↑↑↑M↑↑↑↑↑↑↑↑↑↑↑↑↑L↑↑↑↑↑↑↑↑↑↑↑↑K↑↑↑↑↑↑↑↑↑↑↑J↑↑↑↑↑↑↑↑↑↑I↑↑↑↑↑↑↑↑↑H↑↑↑↑↑↑↑↑G↑↑↑↑↑↑↑F↑↑↑↑↑↑E↑↑↑↑↑D↑↑↑↑C↑↑↑B↑↑A, where z = 26, y = 25, x = 24 ... c = 3, b = 2, and a = 1. This term was coined by DemonSlayer, or Googology Wiki User:I am a McCree God. A good lower bound for this is the 26th ackermann number.
==Approximations==
Notation 	Lower bound 	Upper bound
Arrow notation 	\(26\uparrow^{26}26\) 	\(26\uparrow^{27}26\)
Chained arrow notation 	\(26\rightarrow 26 \rightarrow 26\)	\(26\rightarrow 26 \rightarrow 27\)
BEAF & Bird's array notation 	{26,26,26} 	{26,26,27}
Hyperfactorial array notation	26![1] 	27![1]
Hyper-E notation 	E26##26 	E26##27
Fast-growing hierarchy 	\(f_{\omega}(26)\) 	\(f_{\omega}(27)\)
Hardy hierarchy 	\(H_{\omega^\omega}(26)\) 	\(H_{\omega^\omega}(27)\)
Slow-growing hierarchy 	\(g_{\varphi(\omega,0)}(26)\) 	\(g_{\varphi(\omega,0)}(27)\)
== References ==
Category:Numbers
Category:Up-arrow notation level