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I have been obliged to find ways to make numbers grow faster and faster. We liked the cleverness of Kieran’s “gar-” prefix.
—Alistair Cockburn

Gar- is a prefix invented by the then-six year old Kieran Cockburn, to indicate the number multiplied by itself that many times. Alistair pointed out that the gar- prefix on a number simply indicates its square: gar-n = n2.

It is a backformation of gargoogolplex, which Kieran explicitly stated it to be the square of a googolplex, without using the term "square".

## Examples

• gar(1) = 1 = 1×1
• gar(2) = 4 = 2×2
• gar(3) = 9 = 3×3
• gar(4) = 16 = 4×4
• gar(5) = 25 = 5×5
• gar(6) = 36 = 6×6
• gar(7) = 49 = 7×7
• gar(8) = 64 = 8×8
• gar(9) = 81 = 9×9
• gar(10) = 100 = 10×10
• gar(100) = 10,000 = 100×100
• gar(1,000) = 1,000,000 = 1,000×1,000
• gar(googol) = 10200
• gar(googolplex) = 102×10100
• gar(gar(n)) = (n2)2 = n4

## In googological notations

Notation Expression
Fast-growing hierarchy less than $$f_2(n)$$
Hardy hierarchy less than $$H_{\omega^2}(n)$$
Slow-growing hierarchy $$g_{\omega^2}(n)$$ (exact)
The Q-supersystem $$Q_2(n)$$ (exact)