In PHP, numbers are a data type used to represent numerical values. There are three main types of numbers in PHP: integers, floating-point numbers, and doubles.

- Integers are whole numbers that do not have a decimal point, and they can be positive, negative, or zero. Here is an example of an integer in PHP:

`$num = 42;`

- Floating-point numbers and doubles are numbers with decimal points. Floating-point numbers have a smaller range of values and are less precise than doubles. Here are examples of a floating-point number and a double in PHP:

```
$float = 3.14;
$double = 1.23456789;
```

In addition to these basic number types, PHP also provides a wide range of functions for working with numbers. Here are some examples of commonly used number functions in PHP:

- is_numeric() – Checks if a value is a number

```
$num = 42;
if (is_numeric($num)) {
echo "This is a number";
}
```

In this example, the is_numeric() function is used to check if the variable $num contains a numeric value. If it does, the message “This is a number” is printed to the screen.

- rand() – Generates a random number

```
$random_num = rand(1, 100);
echo $random_num;
```

In this example, the rand() function is used to generate a random number between 1 and 100. The number is stored in the $random_num variable and printed to the screen.

- number_format() – Formats a number with thousands separators

```
$num = 123456789;
echo number_format($num); // Output: 123,456,789
```

In this example, the number_format() function is used to format the number 123456789 with thousands separators. The function returns the formatted number as a string.

In PHP, infinity is a special value that represents a number that is too large to be represented as a normal number. The infinity value is used to represent numbers such as the result of dividing a non-zero number by zero, or the result of calculating the logarithm of zero.

Here is an example of using the INF constant to represent infinity in PHP:

```
$large_number = 1.0e1000;
if ($large_number == INF) {
echo "This number is too large!";
}
```

In this example, the variable $large_number is assigned a very large number using scientific notation. The if statement checks if the value of $large_number is equal to the constant INF, which represents infinity. If the value is infinity, the message “This number is too large!” is printed to the screen.

PHP also provides a negative infinity value, represented by the constant -INF, which is used to represent negative numbers that are too large to be represented normally.

Here is an example of using the -INF constant to represent negative infinity in PHP:

```
$negative_large_number = -1.0e1000;
if ($negative_large_number == -INF) {
echo "This number is too small!";
}
```

In this example, the variable $negative_large_number is assigned a very large negative number using scientific notation. The if statement checks if the value of $negative_large_number is equal to the constant -INF, which represents negative infinity. If the value is negative infinity, the message “This number is too small!” is printed to the screen.

In summary, infinity is a special value in PHP that represents a number that is too large to be represented normally. The constant INF is used to represent positive infinity, and the constant -INF is used to represent negative infinity. These values can be used in mathematical calculations and comparisons to handle large or special cases.

In PHP, NaN (Not a Number) is a special value that represents an undefined or unrepresentable value resulting from a mathematical operation. The NaN value is used to represent the result of calculations that are mathematically undefined, such as dividing zero by zero or taking the square root of a negative number.

Here is an example of using the NAN constant to represent NaN in PHP:

```
$undefined_value = 0 / 0;
if (is_nan($undefined_value)) {
echo "This value is undefined!";
}
```

In this example, the variable $undefined_value is assigned the result of dividing zero by zero, which is mathematically undefined. The is_nan() function checks if the value of $undefined_value is NaN. If the value is NaN, the message “This value is undefined!” is printed to the screen.

PHP also provides a few other functions to work with NaN values, such as the is_nan() and the nan() function.

Here is an example of using the nan() function to create a NaN value in PHP:

```
$undefined_value = nan("");
if (is_nan($undefined_value)) {
echo "This value is undefined!";
}
```

In this example, the nan() function is used to create a NaN value. The is_nan() function checks if the value of $undefined_value is NaN. If the value is NaN, the message “This value is undefined!” is printed to the screen.

In summary, NaN is a special value in PHP that represents an undefined or unrepresentable value resulting from a mathematical operation. The constant NAN is used to represent NaN, and the is_nan() function is used to check if a value is NaN. These values can be used in mathematical calculations and comparisons to handle undefined or special cases.

In PHP, numerical strings are strings that contain a numerical value. PHP can automatically convert a string that contains a numerical value to a number, which can then be used in mathematical calculations.

Here is an example of using a numerical string in PHP:

```
$num_str = "42";
$result = $num_str + 5;
echo $result; // Output: 47
```

In this example, the variable $num_str is assigned the string “42”, which contains a numerical value. The $num_str variable is then used in a mathematical calculation, where it is added to the number 5. Because PHP can automatically convert a string that contains a numerical value to a number, the calculation works correctly and the result is 47.

PHP also provides functions to convert numerical strings to numbers, such as the intval() and floatval() functions.

Here is an example of using the intval() function to convert a numerical string to an integer in PHP:

```
$num_str = "42";
$num_int = intval($num_str);
echo $num_int; // Output: 42
```

In this example, the intval() function is used to convert the string “42” to an integer. The resulting integer value is assigned to the variable $num_int and printed to the screen.

Here is an example of using the floatval() function to convert a numerical string to a floating-point number in PHP:

```
$num_str = "3.14";
$num_float = floatval($num_str);
echo $num_float; // Output: 3.14
```

In this example, the floatval() function is used to convert the string “3.14” to a floating-point number. The resulting floating-point value is assigned to the variable $num_float and printed to the screen.

In summary, numerical strings are strings that contain a numerical value in PHP. PHP can automatically convert a numerical string to a number, which can then be used in mathematical calculations. Additionally, PHP provides functions to convert numerical strings to specific types of numbers, such as the intval() and floatval() functions.

In PHP, it is possible to cast strings and floats to integers using the (int) or (integer) typecast operator. This can be useful when working with numerical values that are stored as strings or floats, but need to be treated as integers for mathematical operations.

Here is an example of casting a string to an integer in PHP:

```
$num_str = "42";
$num_int = (int) $num_str;
echo $num_int; // Output: 42
```

In this example, the (int) typecast operator is used to cast the string “42” to an integer. The resulting integer value is assigned to the variable $num_int and printed to the screen.

Here is an example of casting a float to an integer in PHP:

```
$num_float = 3.14;
$num_int = (int) $num_float;
echo $num_int; // Output: 3
```

In this example, the (int) typecast operator is used to cast the floating-point number 3.14 to an integer. The resulting integer value is assigned to the variable $num_int and printed to the screen. Note that when casting a float to an integer, the decimal portion of the number is truncated.

It’s important to note that when casting a non-numeric value to an integer, the result will be 0. Here’s an example:

```
$text = "Hello, world!";
$num_int = (int) $text;
echo $num_int; // Output: 0
```

In this example, the string “Hello, world!” is cast to an integer using the (int) typecast operator. Because the string does not contain a numerical value, the resulting integer value is 0.

In summary, casting strings and floats to integers in PHP can be accomplished using the (int) or (integer) typecast operator. When casting a non-numeric value to an integer, the result will be 0.

By understanding the basics of numbers and the functions available for working with them, you can create powerful and dynamic applications in PHP.