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Do numbers go on forever?
The question is a bit vague. The set of all natural numbers N (0,1,2,...) has no 'end', there is no 'largest number', in other words: it has an infinite amount of elements. The set of all real numbers R (which includes -2,sqrt(3), pi, e, 56/8, etc.) als has infinitely many elements, but there is a difference between the two: N is a countable set (you can 'count' all the elements), but R is not. If you want to know more about this, you should search after terms like cardinality, countable set, aleph, ...
What is a subset of R x R?
A set of ordered pairs (x, y) where x and y are real numbers.
Is every irrational number a complex number?
Yes! Every complex number z is a number, z = x + iy with x and y belonging to the field of real numbers. The real number x is called the real part and the real number y that accompanies i and called the imaginary part. The set of real numbers is formed by the meeting of the sets of rational numbers with all the irrational, thus taking only the complex numbers with zero imaginary part we have the set of real numbers, so then we have that for any irrational r is r real and complex number z = r + i0 = r and we r so complex number. So every irrational number is complex.
Show that the set of all real numbers is an abelian group with respect to addition?
Sure thing, honey. The set of all real numbers is indeed an abelian group under addition. It's closed because adding two real numbers gives you another real number. It's associative because math plays nice like that. The identity element is 0, and every real number has an inverse (just slap a negative sign in front of it). Plus, addition is commutative, so you can add those numbers in any order and still get the same result. Voilà, you've got yourself an abelian group!
What is the definition of real positive numbers?
A positive real number is any natural, integer, rational, or irrational number x such that x>0. In other words, the real numbers indicated by with or without positive sign (+) is known as Positive Real Number. Positive Real numbers are indicated by R+ mathematically.For example R+ = {1, 2, 3, 4, 5, .....}
