Can you append strings to variables in PHP?

This is because PHP uses the period character . for string concatenation, not the plus character +. Therefore to append to a string you want to use the .= operator:

for ($i=1;$i<=100;$i++)
{
    $selectBox .= '<option value="' . $i . '">' . $i . '</option>';
}
$selectBox .= '</select>';

In PHP use .= to append strings, and not +=.

Why does this output 0? [...] Does PHP not like += with strings?

+= is an arithmetic operator to add a number to another number. Using that operator with strings leads to an automatic type conversion. In the OP's case the strings have been converted to integers of the value 0.

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More about operators in PHP:

• Reference - What does this symbol mean in PHP?
• PHP Manual – Operators

PHP syntax is little different in case of concatenation from JavaScript. Instead of (+) plus a (.) period is used for string concatenation.

<?php

$selectBox = '<select name="number">';
for ($i=1;$i<=100;$i++)
{
    $selectBox += '<option value="' . $i . '">' . $i . '</option>'; // <-- (Wrong) Replace + with .
    $selectBox .= '<option value="' . $i . '">' . $i . '</option>'; // <-- (Correct) Here + is replaced .
}
$selectBox += '</select>'; // <-- (Wrong) Replace + with .
$selectBox .= '</select>'; // <-- (Correct) Here + is replaced .
echo $selectBox;

?>