# Algebra symbology guidance for Ethereum Yellow Paper

There are numerate people who have limited experience in interpreting the algebra used in computer science papers. Therefore, it would be most useful if there were a list of all algebraic symbols used in the Yellow Paper, along with their definition as applied in the paper.

There is of couse this guide, however, for some of the symbols, there are multiple interpretaions.

Please list the symbols used and define their meaning. My understanding is as in my answer below. I've used bold italics where I'm particularly unsure. Please point out where I am wrong.

EDIT - I've posted the list as a community wiki.

• Good idea. You should take the list and post it as an answer to your own question. – Nick Johnson Jun 14 '16 at 15:13
• If you make the answer a community wiki, it will be easy for people to add their own definitions to your answer – Tjaden Hess Jun 14 '16 at 15:58
• Is this asking for guidance of the notation such as Gavin's use of lowercase sigma for state transitions, or was it intended as only the definitions of the more general use mathematical notation as given below? – bekah Nov 25 '16 at 21:01
• @bekah a complete list of all the character's and their meaning would be useful and could be added here (or another question asked). I was mainly looking for the mathemtical notation originally. – atomh33ls Nov 25 '16 at 21:35
• *characters (!) – atomh33ls Dec 26 '19 at 13:15

Univerally recognised mathematical symbols and their name/meaning

is defined as/is equivalent to

is equal to

is not equal to

$\parallel...\parallel$ size (length) of

is in the following set

is not in the following set

for all

union (common elements in adjacent sets)

and

such that

set

function or tuple

array indexing

or (e.g. eq 11), Unsure for equations 24 and 29

greater than

subtraction

summation

either or --- generally used to denote cases, for example piecewise functions with behaviour like 'if this, that. Otherwise, this different thing'.

no. bytes of (e.g. eq 96)

floor; lowest element in

ceiling; highest element in

exclusive or

real numbers greater than or equal to a and less than b

empty set

sequence concatenation (e.g. equations 166,227)

there exists

Symbols which have a specific meaning in the Yellow Paper, but are not universally used in general mathematics

𝔹n hash of size n bytes

Handy reference to the symbols. Not sure this is 100% accurate, pull request appreciated.

https://github.com/deepakraous/ethereum-spec/tree/master/symbols