Editing 2835: Factorial Numbers
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==Explanation== | ==Explanation== | ||
| − | A {{w|factorial}} is a product of positive integers. For instance, four factorial, written '4!', means 4×3×2×1=24. | + | {{incomplete|Revised but needs review from an actual mathematician. Also, are there any practical uses for factorial numbers? Do NOT delete this tag too soon.}} |
| + | -> There aren't any practical uses for it, mostly because it uses 9 bases, which would take many years of numerical base training.-> | ||
| + | A {{w|factorial}} is a product of positive integers. For instance, four factorial, written '4!', means: <math>4×3×2×1=24</math>. | ||
The "base" of a numbering system defines which numbers it uses as digits and what each place value in a number means. For example, in decimal numbers (base 10), the digits go from 0 to 9, and place values are ones, tens, hundreds, etc. So "137" means 1×100 + 3×10 + 7×1 = 137. Numbers can also be written in other bases, such as binary (base 2, using the digits 0 and 1 and place values of 1, 2, 4, 8...) or octal (base 8, using the digits 0-7 and place values of 1, 8, 64, and so on). Using different bases is uncommon, but is sometimes useful in computer science. | The "base" of a numbering system defines which numbers it uses as digits and what each place value in a number means. For example, in decimal numbers (base 10), the digits go from 0 to 9, and place values are ones, tens, hundreds, etc. So "137" means 1×100 + 3×10 + 7×1 = 137. Numbers can also be written in other bases, such as binary (base 2, using the digits 0 and 1 and place values of 1, 2, 4, 8...) or octal (base 8, using the digits 0-7 and place values of 1, 8, 64, and so on). Using different bases is uncommon, but is sometimes useful in computer science. | ||
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In the comic, [[Cueball]] proposes a {{w|factorial number system}}, where the base ''changes'' for each place value - the first digit can be 0 or 1, the next digit can be 0, 1, or 2, the third can be 0, 1, 2, or 3, and so on. Each place value is the factorial of the base. So the number 137 in base 10 could be written as 10221, meaning 1×5! + 0×4! + 2×3! + 2×2! + 1×1!. While this numbering system is technically usable and can express any number, it seems excessively complicated, and the only reason Cueball gives for using it is that he thinks large digits like 9 should only be used in vast numbers (9 would not be used unless the number was at least 9 digits long, or over 3.2 million in decimal). This is a silly reason for using a new numbering system,{{cn}} so the math department thinks this is a prank, and has security throw him out. | In the comic, [[Cueball]] proposes a {{w|factorial number system}}, where the base ''changes'' for each place value - the first digit can be 0 or 1, the next digit can be 0, 1, or 2, the third can be 0, 1, 2, or 3, and so on. Each place value is the factorial of the base. So the number 137 in base 10 could be written as 10221, meaning 1×5! + 0×4! + 2×3! + 2×2! + 1×1!. While this numbering system is technically usable and can express any number, it seems excessively complicated, and the only reason Cueball gives for using it is that he thinks large digits like 9 should only be used in vast numbers (9 would not be used unless the number was at least 9 digits long, or over 3.2 million in decimal). This is a silly reason for using a new numbering system,{{cn}} so the math department thinks this is a prank, and has security throw him out. | ||
| − | In the title text, someone points out that a factorial number system needs more and more digits for each place value. The tenth digit in a factorial number would be in base 11, which needs 11 possible digits, and 0-9 only provides 10. In bases higher than 10, you can use letters to represent higher digits. For example, hexadecimal (base 16) goes from 0 to 9, then from A to F. It would be reasonable to do the same thing for higher bases in factorial numbers. Instead, Cueball says that it's simply illegal to write numbers larger than about 3.6 million, the largest you can go without using a base greater than 10. This is an absurd limitation, as other numbering systems can go as high as you like. | + | In the title text, someone points out that a factorial number system needs more and more digits for each place value. The tenth digit in a factorial number would be in base 11, which needs 11 possible digits, and 0-9 only provides 10. In bases higher than 10, you can use letters to represent higher digits. For example, hexadecimal (base 16) goes from 0 to 9, and then from A to F. It would be reasonable to do the same thing for higher bases in factorial numbers. Instead, Cueball says that it's simply illegal to write numbers larger than about 3.6 million, the largest you can go without using a base greater than 10. This is an absurd limitation, as other numbering systems can go as high as you like. |
The number at the top of Cueball's presentation, 353011, is 3×6! + 5×5! + 3×4! + 0×3! + 1×2! + 1×1! which gives the decimal value of 2835, the number of the comic. | The number at the top of Cueball's presentation, 353011, is 3×6! + 5×5! + 3×4! + 0×3! + 1×2! + 1×1! which gives the decimal value of 2835, the number of the comic. | ||
| − | Cueball's examples of numbers written in | + | Cueball's examples of numbers written in factoradic appear as sequences [https://oeis.org/A007623 A007623] in the OEIS. |
==Transcript== | ==Transcript== | ||
