- #1
FAS1998
- 50
- 1
How can you prove that
##f(x)=g(x) \Leftrightarrow f(x)+C=g(x)+C##
##f(x)=g(x) \Leftrightarrow f(x)+C=g(x)+C##
What do you mean by "elements"?fresh_42 said:I can't as long as I don't know where your elements are taken from.
##f(x),g(x),C##FAS1998 said:What do you mean by "elements"?
This is what I meant.fresh_42 said:##f(x),g(x),C##
If they were, as usual, from ##\mathbb{R}##, then the answer would be: because ##(\mathbb{R},+)## is a group. But if you had defined addition differently on some set, then there is not enough information about it.
Being in a group means existence of an additive inverse, -C.FAS1998 said:I just looked over the wikipedia page for groups and now understand why ##(\mathbb{R},+)## is a group, but why does belonging to a group imply reversibility?
##x \longmapsto e^x## or ##x \longmapsto x^n## e.g. by the theorem of invertible functions or in general step by step. They aren't operations anymore, just other functions.FAS1998 said:How would we prove the reversibility of other operations such as exponentiation (for values >= 0), that don't belong to groups?
"Proof of Addition Reversibility" is a mathematical concept that states that if two numbers are added together, the result can be reversed by subtracting one of the numbers from the sum.
"Proof of Addition Reversibility" is important because it is a fundamental property of addition that allows us to check our calculations for accuracy. It also helps us understand the relationship between addition and subtraction.
"Proof of Addition Reversibility" can be demonstrated by using a simple example, such as 3 + 5 = 8. This can be reversed by subtracting 3 from 8, giving us 8 - 3 = 5, which is the other original number in the addition equation.
Yes, "Proof of Addition Reversibility" applies to all numbers, including whole numbers, fractions, and decimals. As long as the two numbers being added together are real numbers, the result can be reversed by subtraction.
"Proof of Addition Reversibility" is used in everyday life, such as when balancing a checkbook or calculating change when making a purchase. It is also used in more complex mathematical concepts, such as algebra and calculus.