I know what an additive inverse is,(5,-5 2,-2) but what I dont get is why its called the additive inverse. If you take a number like -5 then shouldnt the additive inverse be correctly called 10 to get 5? because its the add-itive inverse(opposite).
Say you start with any number, say 20, now you add say 7 to it and get the answer 27. What would you add to 27 to get back the original number 20? Answer: -7. This number -7 is called theadditive inverse of 7" because adding itundoes" what adding 7 does. Similarly for any other number.
In addition, 0 is theadditive identity" in the sense that N+ additive inverse = N Partly this comes from the idea that themultiplicative identity" is 1 since 1*N = N*1 = N The multiplicative inverse of n/m is m/n since n/m * m/n is the multiplicative identity. As you learn more math, you will see these ideas generalize to matrices and groups, so it is perhaps unfair to expect that it makes sense right now. Theadditive inverse" has the property that when you add it to a number, you get theadditive identity"
When you want to find something to ADD to get back to zero. Examples: The additive inverse of 3 is -3. The additive inverse of 4pi - x is x - 4pi. Additive inverses are very basic (axiomatic) definitions of systems of numbers, vectors, sets, whatever. It's really just a fancy way of sayingthe negative of." But, for some other funny number systems (for example, binary... where there are only 1's and 0's), it's not as simple as just putting a negative sign in front. Again thedictionary" definition is: that which you must add to a given value to achieve a sum of zero. Good luck. Don't let the terminology kill you. Most stuff in math is pretty simple. They just like to try to trip you up.
The inverse of an operation is chosen to get the identity of that operation. The identity is the one that when performed on a number (or whatever) doesn't change it. For addition (and subtract which is just adding negatives) that identity is 0. Anything ± 0 is anything. So if you choose something like 5 then you want to know what the solution to 5 + n = 0 is. Inversion of operations (and functions) in math isn't the same thing as the word inverse itself. To invert something is to literally turn it over. In math the inverse is the thing that undoes. For mathematics when something is undone the result is the identity. For multiplication the identity is 1 so the inverse in multiplication is the reciprocal because it satisfies xn = 1 n = 1/x x(1/x) = 1 For functions the identity is x because if you have a function y = f(x) then if you plug in x you'll get back y. So the inverse function f??(x) will give back x when applied so that f(f??(x)) = x Since composition is the operation here the other way must also be satisfied to be a valid inverse, that is f??(f(x)) = x This idea also goes for matrices and other constructions in math. I hope this helped or was at least mildly interesting. Good luck!
The additive identity is 0. It is called that because it is the only number where you can add it to any other number and get the same thing back. Now, by definition, the additive inverse of a number is what you have to add to that number to get the additive identity. In other words what you have to add to the number to get 0. So the additive inverse of 5 is -5 and the additive inverse of -2 is 2, for example. Side note: You can do the same thing in the multiplicative sense too. The multiplicative identity would the the number that, when you multiply it by any other number, gives you the same thing back. So the multiplicative identity is 1. Thus the multiplicative inverse of a number is what you have to multiply by that number to get the multiplicative identity, in other words what you have to multiply by that number to get 1. So for example the multiplicative inverse of 2 is 1/2 and the multiplicative inverse of -5 is -1/5. The only number without a multiplicative inverse is 0.
