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Transmathematics is a proposed extension of traditional mathematics that redefines division by zero as a valid operation. Unlike standard arithmetic, where division by zero is undefined and considered an error, transmathematics introduces new number entities: infinity (∞) as number, that can be positive, negative, imaginary or negative imaginary, and nullity (Φ), to create a total arithmetic system in which division is always defined.^[1] It has recieved many critics because any number satisfies 0 : 0.^[2] It was created by James A. D. W. Anderson^{[3][circular reference]}.^[4]

Transmathematics is based on ordinary mathematical principles, but it removes the prohibition against dividing by zero. In doing so, it introduces new numbers, called transreal numbers:
Positive Infinity is defined as 1 divided by 0.^[5][6] Every positive number divided by 0 results in positive infinity.^[1] It is explained by Anderson as "If you place an infinite number of grams on one side of a scale, it will always be heavier than the other side, regardless of how much weight is added there."^[1][7] It is represented as "∞" or "+∞".
Negative Infinity is defined as -1 divided by 0^[5][6]. Every negative number divided by 0 results in negative infinity.^[1] It is explained by Anderson as "If you place negative infinity grams on one side of a scale, it will always be lighter than the other side, regardless of how much weight is taken from there."^[1][8] It is represented as "-∞".
Nullity is defined as 0 divided by 0^[1][5][9][6]. Every neutral number (zero or nullity) divided by zero results in nullity.^[1] It is explained by Anderson as "If you place nullity grams on one side of a scale, it will always be the same weight as the other side, regardless of how much weight is added or taken from there."^[1][10][11] It is represented as "Φ". Anderson says this number was discovered in 1997.^[1]

• Wheel Theory