predecessor, successor

Predecessor and successor in whole numbers

In this lesson, we will talk about the predecessors and successors of whole numbers in mathematics, what they represent, and how they can be determined. Whole numbers are the basic counting numbers 0, 1, 2, 3, 4, 5, and so on. Other examples of whole numbers are 100, 567, 999, and 1000.  Every whole number has a predecessor and a successor, except the whole number 0 which does not have any predecessor.

Determining a predecessor

A predecessor is a whole number that comes just before a given number. It is one less than that number. If we state: Number 14 is a predecessor to number 15, what can we realize from this statement? We can see that the number 14 is just before the number 15 or it is one less than the number 15. 
The predecessor of a number can be found in two ways. The first way is by counting. For example, we can take the number 15, and we will start counting until the given number: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. The number that we counted just before number 15 is number 14. It is 1 less than 15 and we can say that it is his predecessor. But what if the given number is larger,  and for example, we take the number 165? It is too long to count to 165. For this number, we will determine the predecessor in the other way, and that is by subtracting one from the given number (because we know that the predecessor is one less of the number). It will be 165-1=164. We can state that 164 is the predecessor of 165. 
Now we know how we can determine the predecessor of any number: 

• 258-1=257
• 5673-1=5672
• 11799-1=11798

Determining a successor

A successor is a whole number that is located immediately after a certain number. It is one more than that number. The successor of the number 15 is number 16. Just like the predecessor, we can determine the successor of a given number by counting, but in that case, the successor is the number that is immediately after the given number. Another method will be adding one to the given number. For example 165+1=166. The number 166 is the successor of the number 165. This method can be applied to all numbers, for instance:

• 2345+1=2346
• 4599+1=4600
• 87432+1=87433

*Tips to remember

• Every whole number has a predecessor and a successor, except the whole number zero, which doesn't have any predecessor
• A predecessor is a number that is one less than a certain number 
• Predecessor = given number − 1
• A successor is a number that is one more than a certain number 
• Successor = given number + 1

The table below represents examples of predecessors and successors of given numbers

Predecessor (given number − 1)	Number	Successor (given number + 1)
99	100	101
230	231	232
598	599	600
998	999	1000
5674	5675	5676