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What do you mean by countably infinite and infinite?
Countably infinite means you can set up a one-to-one correspondence between the set in question and the set of natural numbers. It can be shown that no such relationship can be established between the set of real numbers and the natural numbers, thus the set of real numbers is not "countable", but it is infinite.
Natural numbers are part of every other category of number except?
irrational numbers
Use of natural number in real life?
natural numbers are used in real life for counting, adding, subtracting and even for calculting money purposes
What property states that between any two real numbers there is another real number?
It is the fact that real numbers are infinitely dense.
Difference between real and rational number?
Rational numbers are numbers that can be written as a fraction. Real numbers are any number, including irrationals.
Are natural numbers real numbers?
Yes, all natural numbers are real numbers. Natural numbers are a subset of real numbers, so not all real numbers are natural numbers.
Are real numbers natural numbers?
No. Natural numbers are a proper subset of real numbers.
Are real numbers a subset of natural numbers?
No because natural numbers are a subset of real numbers
What is the relation between integers natural numbers whole numbers rational and irrational numbers?
Natural numbers = Whole numbers are a subset of integers (not intrgers!) which are a subset of rational numbers. Rational numbers and irrational number, together, comprise real numbers.
What is the difference between natural infinite numbers and real infinite numbers?
A natural number is a counting number, such as 1, 2, 3. There are also known as whole numbers and integers. They can be infinitely large. A real number is a number, possibly a natural number, but more possibly not, because there are an infinite number of real numbers that lie between any two natural numbers, such as 1, 1.1, 1.11, 1.111, 111112, etc, ad infinitum. Real numbers can also be infinitely large.
Can a number be a natural number and a real number?
All natural numbers are also real numbers, but all real numbers are not necessarily natural numbers because natural numbers are positive whole numbers. Real numbers are any number on the number line, which includes irrational numbers like pi and sqrt2. Thus only the positive natural numbers are both natural and real. Hope this is not too long-winded!
What do you mean by countably infinite and infinite?
Countably infinite means you can set up a one-to-one correspondence between the set in question and the set of natural numbers. It can be shown that no such relationship can be established between the set of real numbers and the natural numbers, thus the set of real numbers is not "countable", but it is infinite.
What are all the natural numbers?
All the positive real numbers are natural numbers.
What is a natural number that is not real?
The set of Natural Numbers is the set of 'counting numbers' {1,2,3,4,....}. All of them are also real numbers.
Is a natural number the same as a real number?
No. Natural numbers are a very small subset of real numbers.
Are natural numbers a subset of real numbers?
Yes.
What are the differences between real numbers and imaginary numbers?
The set of real numbers is not closed under powers. That is to say, there are some equations of the form y = xa which do not have a solution within the set. Typical example: x is negative, a = 0.5
