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 Apr27 comment role of definitions in proofs Definitions do not, as you say, "define objects." Instead, as any dictionary shows, they define the words we use for objects. Where they come from would be a matter of accepted convention. Apr24 comment Could somebody please help me prove this using the properties of real numbers introduced in elementary algebra? Is it logically correct to state "1 is its own reciprocal because 1 * 1 = 1." And to prove this by the identity property of multiplication: a * 1 = a? Given that we know, by definition, reciprocals are two numbers whose product is 1. Apr24 suggested rejected edit on Could somebody please help me prove this using the properties of real numbers introduced in elementary algebra? Apr24 comment Is an empty parenthesis a valid mathematical expression? Short answer: no. Apr24 comment Could somebody please help me prove this using the properties of real numbers introduced in elementary algebra? In the equation 1/1 = 1 the right hand side is called a fraction in simplest form. Does that mean all the integers are fractions in simplest form? But a ratio in simplest form must be n/1 for n = integer? Apr23 revised Infinity isn't a Number deleted 1 character in body Apr23 accepted Infinity isn't a Number Apr23 revised what is the definition of Mathematics ? added 52 characters in body Apr23 revised How to simplify this square $(3 \times 4 + 2)^2$? added 115 characters in body Apr23 revised what is the definition of Mathematics ? added 53 characters in body Apr20 comment Finding all possible pairs of positive integer values But, if x is equal to y the ratio is undefined. Apr20 comment Finding all possible pairs of positive integer values Why do you put the "equal to" into your condition: Assume x >= y? Apr19 revised Finding all possible pairs of positive integer values edited tags Apr18 asked Finding all possible pairs of positive integer values Apr16 comment How would multiplying money work? But if that meal has a negative nutritional value "imagine" the complexities ;-) Apr2 awarded Suffrage Mar20 awarded Curious Mar16 awarded Necromancer Feb20 comment A set without the empty set Sometimes textbooks tell the reader that the symbol $\in$ is read "belongs to", how does anything belong to the empty set? Jan5 accepted Is the division property of equality just a special case of the multiplication property?