Overview[]
The Base is a fundamental value used for Ordinals in Ordinal Markup. You can find your current Base where the ([Base Value]) is in the full Ordinal. Specifically, it is the Base in the Hardy Hierarchy that Ordinals are modified as a result of. When a regular number in an Ordinal reaches the value of the Base or higher and the maximize Ordinal button is pressed it turns into Lowercase Omega (ω), then the Ordinal is simplified from there.
Calculating the Base[]
The Base can be reduced via Factor Shifting. The Base is calculated by , where represents the amount of Factor Shifts you have done, is 1 if you are in Challenge 3 or 0 otherwise; is 1 if you are in Challenge 4 or 0 otherwise; is 1 if you are in Challenge 7 or 0 otherwise, is 1 if you have u13 and the Base is normally over 7, and 0 otherwise. Keep in mind that with u23, the Base will be set to 5 no matter what, unless your Ordinal is above ψ(Ω). The current minimum possible Base is 3, and the maximum possible Base is 15.
! Note: | For visual clarity, a table has been provided to show you the Base in certain situations (like during Challenges). |
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Runs | Normal Run | Challenge 3 | Challenge 4 | Challenge 7 | ||||||
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Upgrades | No | u13 | u23 (includes all runs, but only before an Ordinal of ψ(Ω)) | No | u13 | No | u13 | No | u13 | |
Factor Shifts | 0 | 10 | 6 -> 5 | 5 | 15 | 11 | 10 | 6 -> 5 | 15 | 11 |
1 | 9 | 5 | 5 | 14 | 10 | 10 | 6 -> 5 | 15 | 11 | |
2 | 8 | 4 | 5 | 13 | 9 | 10 | 6 -> 5 | 15 | 11 | |
3 | 7 | 7 | 5 | 12 | 8 | 10 | 6 -> 5 | 15 | 11 | |
4 | 6 -> 5 | 6 -> 5 | 5 | 11 | 7 | 10 | 6 -> 5 | 15 | 11 | |
5 | 5 | 5 | 5 | 10 | 6 -> 5 | 10 | 6 -> 5 | 15 | 11 | |
6 | 4 | 4 | 5 | 9 | 5 | 10 | 6 -> 5 | 15 | 11 | |
7 | 3 | 3 | 5 | 8 | 4 | 10 | 6 -> 5 | 15 | 11 |
All values at Base 6 will be 5 if you have u36 (6 (without u36) -> 5 (with u36))
The Effect of the Base[]
Bases are incredibly powerful, and can affect Ordinals by a lot. This is because in the Ordinal, Lowercase Omega (ω) is worth 10 OP regardless the Base. For example the Ordinal ω^{3} would be worth 1000 OP in Bases higher than 3, but in Base 3 ω^{3} would be converted to ω^{ω}, which is worth 1.000e10 base OP.
Base Value | Ordinal Value at 1.000e10 clicks (Maximisation) (Max Ordinal Length at 5) | Base OP Value (Rounded) | 15 | ω^{8}3+ω^{7}13+ω^{6}7+ω^{5}13+ω^{4}10+... | 4.384e8 |
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14 | ω^{8}6+ω^{7}10+ω^{6}12+ω^{5}+ω^{4}6+... | 7.122e8 | |||
13 | ω^{8}12+ω^{7}3+ω^{6}4+ω^{5}9+ω^{4}11+... | 1.235e9 | |||
12 | ω^{9}+ω^{8}11+ω^{7}3+ω^{5}11+ω^{4}9+... | 2.131e9 | |||
11 | ω^{9}4+ω^{8}2+ω^{7}7+ω^{6}+ω^{5}8+... | 4.272e9 | |||
10 | ω^{ω} | 1e10 | |||
9 | ω^{ω+1}2+ω^{ω}7+ω^{8}7+ω^{7}2+ω^{6}6+... | 2.707e11 | |||
8 | ω^{ω+3}+ω^{ω+2}+ω^{ω+1}2+ω^{ω}4+ω^{6}2+... | 1.124e13 | |||
7 | ω^{ω+4}5+ω^{ω+2}2+ω^{ω+1}5+ω^{ω}4+ω^{6}4+... | 5.025e14 | |||
6 | ω^{ω2}4+ω^{ω+5}3+ω^{ω+4}3+ω^{ω+3}2+ω^{ω+2}+... | 4.000e20 | |||
5 | ω^{ω2+4}+ω^{ω2+3}3+ω^{ω2+1}4+ω^{ω2}4 | 1.304e24 | |||
4 | ω^{ω2}2+ω^{ω3+3}+ω^{ω3+2}+ω^{ω3+1}+ω^{ω2+1}2+... | 2.000e100 | |||
3 | ω^{ω22+2}2+ω^{ω22+1}2+ω^{ω22}+ω^{ω2+ω2+2}2+ω^{ω2+ω2+1}+...^{} | 2.210e202 |
Trivia[]
- To reach an Ordinal of ψ(Ω), you need to have a Power Tower of an amount of ω, where represents your Base value. For example, a Base of 3 would require ω^{ωω} and a Base of 5 would need ω^{ωωωω} (impossible).
- A Base of 4 or over makes it impossible to reach an Ordinal of ψ(Ω). This is due to the fact that you would need an Ordinal of at least ω^{ωωω} (in Base 4). This is significantly harder than it seems, and the
game.ord
variable in the game's code would reach its limit far before you would reach ω^{ωωω}, so it is deemed as impossible (for now)