every real number has a decimal expansion?
442933
0 has a decimal expansion, too, so all real numbers have a decimal expansion, and moreover, all of them (except arguably 0) have an infinite decimal expansion (though some also have a finite decimal expansion).
1088130
Irrational, decimal does not terminate and has no repeated pattern. Rational, decimal terminates. Irrational, decimal does not terminate and has no repeated pattern.
1091603
All real numbers can be written in decimal form, but some real numbers(irrationals) cannot be written as the fraction of two integers.
1106482
Yes, every real number has a binary representation, just like every real number has a decimal (and an octal, and hexadecimal, and similar for any other base) representation, though only if you allow an infinite number of digits.
216790
The set of real numbers is closed under addition. If you add two real numbers, you will get another real number. There is no possibility of ever getting anything other than another real number.
19803
So if 0 = 1, then (as you proved) all real numbers equal 0, so there are no positive real numbers. So if you can prove that not all numbers are equal, then it's a valid proof.
1215160
The set of real numbers is closed under multiplication. If you multiply two real numbers, you will get another real number. There is no possibility of ever getting anything other than another real number. The set of real numbers is NOT closed under division.
1167698
more ... The type of number we normally use, such as 1, 15.82, −0.1, 3/4, etc. Positive or negative, large or small, whole numbers or decimal numbers are all Real Numbers. They are called "Real Numbers" because they are not Imaginary Numbers.
149742
The real numbers include natural numbers or counting numbers, whole numbers, integers, rational numbers (fractions and repeating or terminating decimals), and irrational numbers. The set of real numbers is all the numbers that have a location on the number line.
1359958
Yes. Every real number is necessarily a rational number or an irrational number.
525092
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line. ... The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2 (1.41421356..., the square root of 2, an irrational algebraic number).
1077659
Irrational numbers can also be expressed as non-terminating continued fractions and many other ways. As a consequence of Cantor's proof that the real numbers are uncountable and the rationals countable, it follows that almost all real numbers are irrational.
1076539
1 is a whole. All decimals are part of 1. The closer a decimal is to 1, the larger the decimal is. Let's use place value to figure out which number is closer to one then compare the values.
650100
No, every whole number is a rational number as it can be written as a fraction. ... However, pi can not, because it cannot be expressed as a fraction, so it is irrational. In conclusion, all fractions, repeating decimals, terminating decimals, and integers are rational numbers.
1311781
(i) 23 is not a perfect square values so that, it is an irrational number. The decimal expansion of above number is terminating, so that it is a rational number. The decimal expansion of above number is non-terminating recurring, so that, it is a rational number.
888193
Then we simply extend this to all real numbers and all the whole numbers themselves, and since the real numbers, as demonstrated above, between any two whole numbers is countable, the real numbers are the union of countably many countable sets, and thus the real numbers are countable.
1081054
So if your decimal value is 5.627, the whole number is 5; if your decimal value is 9.5, the whole number is 9; and so on.