Table of Contents
What is a Decimal?
A decimal is a number that is written using a base 10 number system. This means that the number is composed of 10 digits, 0-9, and that the value of each digit is based on its position in the number. For example, the number 987.654 can be decomposed into its individual digits as 9, 8, 7, 6, 5, 4. The value of each digit is based on its position in the number. The 9 is worth 9 times 10^0, or 9. The 8 is worth 8 times 10^1, or 80. The 7 is worth 7 times 10^2, or 700. The 6 is worth 6 times 10^3, or 6000. The 5 is worth 5 times 10^4, or 50000. The 4 is worth 4 times 10^5, or 400000.
What is Terminating Math Definition?
Terminating math is a type of math in which the sequence of operations eventually leads to a result that can be expressed in a finite number of symbols. For example, the sequence of operations 1 + 1 + 1 can be expressed as 3, and the sequence of operations 1 + 1/2 + 1/4 can be expressed as 2.5.
Recognising a Terminating Decimal
A terminating decimal is a decimal that has a finite number of digits that repeat forever, such as 0.33333…
Recognising a terminating decimal is easy – you just need to look for a pattern in the digits. For example, in 0.33333…, the 3’s keep appearing. This means that the decimal will keep going until it reaches 3 digits, and then it will repeat those same 3 digits forever.
Other terminating decimals include 0.22222…, 0.14286…, and 0.09091…
What is Non-Terminating Meaning?
Non-terminating means that a process or sequence of events does not have an end. This can be due to an infinite loop, or an event that keeps happening without any foreseeable end.
Theorem
There exists a unique function that maps every real number to its square root.
Proof
We will use mathematical induction to prove that the function exists and is unique.
The function exists: We will show that there is a function that maps every real number to its square root. We can define such a function by simply taking the square root of each number in the domain.
The function is unique: We will show that the function is unique by demonstrating that no other function can map every real number to its square root. Suppose there were two functions that did this. We would then have two square roots for every number. But this is impossible, because the square root of a number is unique.
