Number System - Successor and Predecessor

The Successor of a number is the number that comes immediately after it. You can find it by adding $1$ to the given number. On a horizontal number line, the successor is always one unit to the right of the number.

The Predecessor of a number is the number that comes immediately before it. You can find it by subtracting $1$ from the given number. Visually, on a number line, the predecessor is located one unit to the left of the number.

In the system of whole numbers, the number $0$ is the smallest number and does not have a predecessor because no whole number exists before it.

When finding the successor of a number ending in $9$, like $9,999$, a carry-over occurs across place values. For example, the successor of $9,999$ is $10,000$, where the digit $9$ in the thousands place changes as well, much like a car odometer rolling over.

When finding the predecessor of a number ending in $0$, like $5,000$, you must 'borrow' from the higher place values. The predecessor of $5,000$ is $4,999$. Imagine the place value blocks being broken down into smaller units to subtract $1$.

Any number (except $0$) sits exactly between its predecessor and its successor. This can be expressed as the sequence: $Predecessor \to Number \to Successor$. For example, in the sequence $455, 456, 457$, $455$ is the predecessor and $457$ is the successor of $456$.

For large 5-digit and 6-digit numbers, the rules remain the same. The successor of $1,25,340$ is $1,25,341$, and the predecessor is $1,25,339$. Always focus on the ones place first.