Caret confused with other chevron-shaped characters, such as or , which may occasionally be called carets, too. The caret was originally and continues to be used in handwritten form as a proofreading mark to indicate where a punctuation mark, word, or phrase should be inserted into a document. The term comes from the Latin , "it lacks", from , "to lack; to be separated from; to be free from". The caret symbol is written below the line of text for a line-level punctuation mark, such as a comma, or above the line as an inverted caret (cf. ) for a higher
Levi-Civita symbol or not. In index-free tensor notation, the Levi-Civita symbol is replaced by the concept of the Hodge dual. In a context where tensor index notation is used to manipulate tensor components, the Levi-Civita symbol may be written with its indices as either subscripts or superscripts with no change in meaning, as might be convenient. Thus, one could write In these examples, superscripts should be considered equivalent with subscripts. Summation symbols can be eliminated by using Einstein notation, where an index repeated between two or more terms indicates summation over that index. For example, In the following examples, Einstein notation is