Is nothing, or what might otherwise be called the null value or zero a number? Being a mathematics major with aspirations of going on to graduate school I feel that I encounter it far to often in too many contexts to be able to make a complete philosophical argument as to why it should or should not be considered a number. However, in the more abstract concepts of mathematics it definitely has a purpose. As the identity, 0 provides the same service to addition as 1 provides to multiplication.
The identity in other circumstances can be anything that maps each object to itself in a group of objects acted upon by an operator. For example if you were to look at a triangle the ways you could rotate or flip it so that the triangle looks positioned the same whether or not the corners have exchanged places, the identity would be to simply not move it. This lack of action can be loosely referred to as nothing, Yet it is something that gives a valid result and so must be included as part of the set of possible actions that make the triangle appear to be the same way.
In a similar fashion I believe that zero is a number simply because it must be categorized with other numbers for the purpose of dealing with no change in addition. It may not be necessarily philosophically appropriate to call it a number, but it is such a mathematical convenience to call it such that it would be almost masochistic to not do so.
Simply put I believe zero is a number because mathematicians call it a number, and they should know. To argue otherwise philosophically would be akin to arguing something doesn't belong in a category that convention determines to be in such a category (which I don't claim to be necessarily faulty). To argue otherwise mathematically would be a contraction of many existent conventions and would probably require a reworking of the whole of mathematics on the most rigorous level.
The identity in other circumstances can be anything that maps each object to itself in a group of objects acted upon by an operator. For example if you were to look at a triangle the ways you could rotate or flip it so that the triangle looks positioned the same whether or not the corners have exchanged places, the identity would be to simply not move it. This lack of action can be loosely referred to as nothing, Yet it is something that gives a valid result and so must be included as part of the set of possible actions that make the triangle appear to be the same way.
In a similar fashion I believe that zero is a number simply because it must be categorized with other numbers for the purpose of dealing with no change in addition. It may not be necessarily philosophically appropriate to call it a number, but it is such a mathematical convenience to call it such that it would be almost masochistic to not do so.
Simply put I believe zero is a number because mathematicians call it a number, and they should know. To argue otherwise philosophically would be akin to arguing something doesn't belong in a category that convention determines to be in such a category (which I don't claim to be necessarily faulty). To argue otherwise mathematically would be a contraction of many existent conventions and would probably require a reworking of the whole of mathematics on the most rigorous level.