Is there any natural number that has no predecessor (chapter 2)?
Introduction:
In mathematics, every natural number except 1 has a predecessor. The predecessor of a natural number n is the number that comes just before n. For example, the predecessor of 5 is 4, and so on. But is there any natural number that has no predecessor?
Explanation:
The answer is no. Every natural number except 1 has a predecessor. To understand why, we can use mathematical induction.
Mathematical induction is a proof technique that is used to prove that a statement is true for all natural numbers. The basic idea of mathematical induction is to prove that the statement is true for the smallest natural number (usually 1), and then show that if the statement is true for any natural number, then it must also be true for the next natural number.
Using mathematical induction, we can prove that every natural number except 1 has a predecessor.
Proof:
1. Base case: The statement is true for n = 2. The predecessor of 2 is 1, which is a natural number.
2. Inductive step: Assume that the statement is true for some arbitrary natural number k. That is, k has a predecessor, which we will call k-1. We want to show that the statement is also true for k+1.
To do this, we note that k+1 is also a natural number, and we can write it as (k+1) = (k) + 1. Since k has a predecessor, we know that k-1 is a natural number. Adding 1 to both sides, we get:
(k-1) + 1 = k
So k is the successor of (k-1). Since k is a natural number, it follows that (k-1) is also a natural number. Therefore, k+1 has a predecessor, namely k.
Conclusion:
We have shown that every natural number except 1 has a predecessor. Therefore, there is no natural number that has no predecessor.
Is there any natural number that has no predecessor (chapter 2)?
1 is the only natural no. that has no predecessor . and according to the question the predecessor of natural no. should be natural.
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