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I know it's very vague, but as I'm only a novice Googologist, I just wanted to know if the general idea is plausible.

Step 1: Create a fast-growing function that outputs not finite numbers, but ordinals

Step 2: Use this function to define a very large ordinal

Step 3: Create a fast-growing function using the fundamental sequence of that ordinal

Step 4: Use this new function to define a very large finite number

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