i've got a question in my math
its wanting to know why is the 1 called the multiplicative identity
multiplying any number by 1 does not change that number
e.g. 56x1 = 56
the number keeps its "identity".
BTW the "additive" identity would be the number 0
The multiplicative identity is a number, denoted by 1 that has the property that:
1*x = x
for all x
You can then prove that there can only exist one number with this property. If you assume that there are two such numbers 1 and 1', then we have:
1*1' = 1'
because 1 is the identity.
But we also have:
1*1' = 1
because 1' is also the identity. So, we see that 1' = 1 and we see that the multiplicative identity is a unique number.
The number 1 is called the multiplicative identity because it has a special property when it is multiplied with any other number.
To understand why 1 is the multiplicative identity, let's look at the definition of the multiplicative identity property. This property states that for any number, when it is multiplied by the multiplicative identity, the result is always the original number. In other words, any number multiplied by 1 will remain unchanged.
Let's take an example. Consider the number 5. When we multiply 5 by 1, we get 5 * 1 = 5. As you can see, the result is the original number 5. This is true for any number we choose. For instance, if we take 7 and multiply it by 1, we get 7 * 1 = 7, which is the same as the original number 7.
This unique property of the number 1 is what makes it the multiplicative identity. It acts as a "neutral" element in multiplication because it does not change the value of other numbers when multiplied by them. Every number, when multiplied by 1, retains its identity.
This property is significant in mathematics because it simplifies calculations and allows us to solve equations and manipulate numbers more easily.