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The grinningold regiment is a series of numbers from E100##100#100#100#100 to E100,000##100,000#100,000#100,000#100,000#3 defined using Extended Hyper-E Notation (i.e. beginning from grinningold and up to grinningolda-dusutetrexigong).[1][2] The numbers were coined by Sbiis Saibian.

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## List of numbers of the regiment

Name of number Extended Hyper-E Notation (definition) Fast-growing hierarchy (approximation)
Grinningold E100##100#100#100#100 $$f_{\omega+3}(100)$$
Grinningolda-sutetrex E100##100#100#100#100#2 $$f_{\omega+3}^2(100)$$
Grinningolda-dusutetrex E100##100#100#100#100#3 $$f_{\omega+3}^3(100)$$
Grinningoldachime E1000##1000#1000#1000#1000 $$f_{\omega+3}(1000)$$
Grinningolda-sutetrexichime E1000##1000#1000#1000#1000#2 $$f_{\omega+3}^2(1000)$$
Grinningolda-dusutetrexichime E1000##1000#1000#1000#1000#3 $$f_{\omega+3}^3(1000)$$
Grinningoldatoll E10,000##10,000#10,000#10,000#10,000 $$f_{\omega+3}(10000)$$
Greegolda-suthrexitoll E10,000##10,000#10,000#10,000#10,000#2 $$f_{\omega+3}^2(10000)$$
Grinningolda-dusutetrexitoll E10,000##10,000#10,000#10,000#10,000#3 $$f_{\omega+3}^3(10000)$$
Grinningoldagong E100,000##100,000#100,000#100,000#100,000 $$f_{\omega+3}(100000)$$
Grinningolda-sutetrexigong E100,000##100,000#100,000#100,000#100,000#2 $$f_{\omega+3}^2(100000)$$
Grinningolda-dusutetrexigong E100,000##100,000#100,000#100,000#100,000#3 $$f_{\omega+3}^3(100000)$$