# What is Base 1?

Base 1 is a numeral system that uses only one symbol to represent natural numbers. It is also known as the unary numeral system or the tally mark system. In base 1, a number N is represented by repeating the symbol N times. For example, using the symbol |, the number 5 is represented as |||||.

Base 1 is different from other positional numeral systems, such as base 10 (decimal) or base 2 (binary), which use multiple symbols and assign different values to them depending on their position. In base 10, for example, the number 123 is represented by using three symbols: 1, 2 and 3, and multiplying them by powers of 10: 1 Ã 10 + 2 Ã 10 + 3 Ã 10. In base 2, the same number is represented by using two symbols: 0 and 1, and multiplying them by powers of 2: 1 Ã 2 + 1 Ã 2 + 1 Ã 2 + 0 Ã 2 + 1 Ã 2 + 1 Ã 2 + 1 Ã 2.

Base 1 does not have a symbol for zero, because zero means the absence of any symbol. Therefore, base 1 is a bijective numeral system, meaning that there is a one-to-one correspondence between natural numbers and their representations. However, some variations of base 1 have been proposed that use two symbols, such as | and O, to represent numbers and zero respectively. In this case, base 1 becomes a binary system with redundant symbols.

Base 1 is mainly used for counting or tallying purposes, such as keeping track of scores or votes. It is also useful for illustrating some mathematical concepts, such as prime numbers or factorization. However, base 1 is not very efficient for arithmetic operations or data storage, because it requires a lot of space and symbols to represent large numbers.

## Advantages and Disadvantages of Base 1

Base 1 has some advantages and disadvantages compared to other numeral systems. Some of the advantages are:

- Base 1 is easy to learn and use, as it only requires one symbol and no rules for arithmetic operations.
- Base 1 is universal and can be understood by anyone, regardless of their language or culture.
- Base 1 is useful for illustrating some mathematical concepts, such as prime numbers, factorization, or the Peano axioms.

Some of the disadvantages are:

- Base 1 is inefficient and impractical for representing large numbers, as it requires a lot of space and symbols.
- Base 1 does not have a symbol for zero, which makes it difficult to express concepts such as nothingness, emptiness, or absence.
- Base 1 does not have a way to represent fractions, decimals, or negative numbers, which limits its applicability to real-world problems.

## Applications of Base 1

Base 1 is mainly used for counting or tallying purposes, such as keeping track of scores or votes. For example, in some sports or games, base 1 is used to indicate the number of points or goals scored by each team or player. In some elections or surveys, base 1 is used to record the number of votes or preferences for each candidate or option.

Base 1 is also used in some fields of science and technology, such as cryptography, computer science, or logic. For example, in cryptography, base 1 can be used to encode messages using a simple substitution cipher. In computer science, base 1 can be used to represent unary languages or automata. In logic, base 1 can be used to define the simplest propositional calculus.

Base 1 can also be used for artistic or creative purposes, such as poetry, music, or art. For example, in poetry, base 1 can be used to create patterns or rhythms based on the repetition of a single sound or syllable. In music, base 1 can be used to compose melodies or harmonies based on a single note or chord. In art, base 1 can be used to create shapes or forms based on a single line or stroke.