Real numbers(F.3)

1. If x is a real number, the inequality x² < 0 has no solution.
TRUE.

(What is meant by real numbers, please give an example.)
You mentioned that this is a form 3 level, then I should tell you, any number that can be represented on the number line is a real number.

Soon you will be promoted to form 4, then you need to learn several classes of numbers, namely, natural numbers (N), integers (Z), rational numbers (Q), real numbers (R), complex numbers (C).

Don't worry about the complexity, they are all very funny and interesting.
=^o^=

More information to help you revise your knowledge from this question, recall the fact that the square of ANY real number MUST BE non-negative, it is at least 0, or even positive.
In terms of mathematical expression, for any real number x, x² ≥ 0.

2. If a, b, c are real numbers such that a - b < a - c, then b > c.
TRUE.

(Also give an example.)
Showing a true statement in mathematics needs a proof, not an example.
Proof:
a - b < a - c
-b < -c [subtracting a from both sides]
c < b [adding b+c to both sides]
b > c [another representation]
proved.


3. If x is a real number, which of the following inequalities has/have no solutions?
(1) x > x
(2) x ≤ x
(3) x² ≤ 0

(Please give example if possible.)

(1) x > x has no solution clearly. You cannot find any x satisfying this inequality.

(2) x ≤ x mean x > x or x = x, where x = x is always true. Therefore, the statement x ≤ x is true for any number x. Therefore, there are infinitely many solution x such that x ≤ x. (Simply speaking, there exist solutions.) A note to you: 123 ≤ 123 is true.

(3) x² ≤ 0
From my words highlighted in pink above, we are sure that for real number x, x² ≥ 0 for sure. Now if both x² ≤ 0 and x² ≥ 0 are to be held, then there is a solution which is x = 0.

Therefore, only (1) has no solution.

[I know that the above is a very long message, but I hope that you can learn something useful here.]

2013-08-27 04:23:37 補充：
多謝 ✡ HYPERCUBE ✡ 正面支持和鼓勵。

=^o^=

+1 for Masterijk !