Question

In a lot of places equality is defined that for two expressions A=B, A=B means that A and B have the same value (A=B). This relationship seems strange as we are slightly abusing use/mention, if '=' denotes a relationship between expressions then in '1+1=2' '1+1' and '2' are denoting themselves.

Doing this seems a little bit strange considering we generally use '2' and '1+1' to denote values themselves.

If we treat equality as a relationship a mathematical object has with itself, it is not that useful, however the variety of the names and what they inform us of is, for example x+1=2 is equivalent to 2=2 but the former is more interesting.

In this way, is the elementary mathematical use of the equals sign essentially just an identity statement?

Answer 1

The equals sign (=) in mathematics represents equality between two expressions and is not simply an identity statement. By performing the same operation on both sides of the equation, the expression remains an equality, allowing us to manipulate equations to solve for unknown variables.

Step-by-step explanation:

The use of the equals sign (=) in mathematics is not simply an identity statement, but rather a representation of equality between two expressions. It is important to note that the equals sign does not denote a relationship between the expressions, but rather states that the two expressions have the same value. For example, in the equation 1+1=2, the expressions '1+1' and '2' are denoting their respective values, not themselves as objects.

When we perform operations on both sides of the equation, as long as the same operation is used, the expression remains an equality. This allows us to manipulate equations and solve for unknown variables. For instance, in the equation x+1=2, we can subtract 1 from both sides to find that x has a value of 1.