In the set of real numbers, the first number greater than -4 is -3. True False?

False,

In the set of integers, this statement is true, however

In the set of real line, there are infinitely many values between ANY two numbers, (called the density theorem, -density of rationals and irrationals))

Hence, the statement is false, because -3 is not the first number greater than -4 on the real line, we don't know the number which is the first number greater than -4, but we know that there are infinitely many numbers between -4 and -3, so -3 is not the first one. it's -3.99999999999999999...... and the decimal goes to infinity, we do not know what the first number greater than -4

False

False. There is NO real number which is "next to" another one.

False.

If we were talking about the set of INTEGERS, then this would be true, but when dealing with real numbers, there is no such thing as "the next number" because the set is uncountable.

False. In the real numbers, there is no "next number" or "first number greater than some other number.
Change "real numbers" to "integers" and it's true.

No. -3.9 is a real number and is closer to -4 than -3.

false

FALSE.... because there are other numbers greater than -4 before - 3.such numbers are 0,-1,-2