Editing Addition (section)

=== Identity element ===
[[File:AdditionZero.svg|right|upright=0.33|thumb|5 + 0 = 5 with bags of dots]]
Adding [[0 (number)|zero]] to any number does not change the number. In other words, zero is the [[identity element]] for addition, and is also known as the [[additive identity]]. In symbols, for every <math> a </math>, one has:{{sfnp|Musser|Peterson|Burger|2013|p=[https://books.google.com/books?id=8jh7DwAAQBAJ&pg=PA90 90]}}
<math display="block"> a + 0 = 0 + a = a. </math>
This law was first identified in [[Brahmagupta]]'s ''[[Brahmasphutasiddhanta]]'' in 628&nbsp;AD, although he wrote it as three separate laws, depending on whether <math> a </math> is negative, positive, or zero itself, and he used words rather than algebraic symbols. Later [[Indian mathematicians]] refined the concept; around the year 830, [[Mahavira (mathematician)|Mahavira]] wrote, "zero becomes the same as what is added to it", corresponding to the unary statement <math> 0 + a = a </math>. In the 12th&nbsp;century, [[Bhāskara II|Bhaskara]] wrote, "In the addition of cipher, or subtraction of it, the quantity, positive or negative, remains the same", corresponding to the unary statement <math> a + 0 = a </math>.{{sfnp|Kaplan|2000|pp=69–71}}
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