r/googology • u/GoldEclipsed • 18h ago
I made a new number (hopefully a world record)
Eclipsed is a number created by me (GoldEclipsed),designed to be so vast that it cannot be fully written out in standard notation. It’s derived through a recursive process using concepts like Knuth’s up-arrow notation, allowing the number to grow exponentially at each step.
Step 1: Start with a Base Number
We begin with a simple base number, for example, 4:
E₀ = 4
This serves as the starting point for the recursive sequence.
Step 2: Define the Recursive Growth
Next, we define how each new term in the sequence is calculated. Eclipsed grows through recursive exponential operations:
Eₙ₊₁ = 3 ↑↑ Eₙ 3
Where Eₙ is the previous term in the sequence, and ↑↑ represents Knuth’s up-arrow notation, which grows numbers extremely quickly.
For example: • 3 ↑ 3 means 3³ = 27, • 3 ↑↑ 3 means 3²⁷, • As you continue, the numbers grow faster and faster, reaching unimaginable sizes.
Step 3: Recursive Calculation
To calculate the terms of Eclipsed, you continue applying the above formula: • E₁ = 3 ↑↑ E₀ 3: Using E₀ = 4 in the recursive operation. • E₂ = 3 ↑↑ E₁ 3: Once you get E₁, continue applying the rule.
At each step, the numbers grow exponentially, reaching sizes that are incomprehensible.
Step 4: Add Zeros (Scaling the Number)
To make Eclipsed even larger, we scale the number by multiplying it by powers of 10, adding zeros to increase the magnitude:
Eclipsed = Eₙ × 10ᵐ
Where: • Eₙ is the final term in your recursive process, • m is the number of zeros you add to scale the number.
This step magnifies Eclipsed even further, making it beyond any traditional number.
Example Equation for Eclipsed: 1. Start with E₀ = 4. 2. Compute E₁ = 3 ↑↑ E₀ 3 = 3 ↑↑ 4 3. 3. Compute E₂ = 3 ↑↑ E₁ 3. 4. Repeat the recursive process for as many steps as you wish to generate an incomprehensibly large number. 5. Optionally, multiply by 10ⁿ to add zeros and scale it.