There are several ways to prove that x*0=0 without relying on the property m(-1)=-m. One approach is to use the definition of multiplication as repeated addition and show that when x is multiplied by 0, the result is always 0. Another method is to use the distributive property and show that when 0 is multiplied by any number, the result is always 0.
Sure, let's take the example of x=5. When 5 is multiplied by 0, we get 5*0=0. This can be shown using the repeated addition method by adding 0 to itself 5 times, or using the distributive property by distributing 0 to each term in the expression 5*0.
No, in order to prove a mathematical statement, we must use some basic properties and axioms. However, it is possible to prove x*0=0 using only fundamental properties such as the definition of multiplication and the commutative and distributive properties.
Proving x*0=0 without using the property m(-1)=-m helps to strengthen our understanding of the fundamental properties of multiplication and the relationships between different numbers. It also allows us to verify that the property m(-1)=-m is not a fundamental axiom, but can be derived from other properties.
No, by the definition of multiplication and the properties of 0, the only possible result of multiplying any number by 0 is 0. This can be verified through examples or by using the properties of multiplication and the fact that x*0=0 can be rewritten as x*(0+0)=x*0+x*0, which simplifies to 0=0.