How to exclude category ID from Looper in Wordpress

Question

I'm trying to exclude 2 (and potentially more) ID's from my loop, that displays all categories that have posts. The category ID's i'm currently trying to exclude are 1 and 19. I'm very new to PHP but have previously been able to fix my issues by searching on the forum but nothing so far has worked.

// Function to create shortcode of all categories
function my_categories_shortcode() { 
 
// extracting categories
$args=array(
  'orderby' => 'name',
  'order' => 'ASC',
)

?><div class="categorylist">
 <?php foreach (get_categories( $args ) as $cat ) : ?>

<a class="categorylink" href="<?php echo get_category_link($cat->term_id); ?>"><img src="<?php echo z_taxonomy_image_url($cat->term_id); ?>" />
<h3 class="categoryname"><?php echo $cat->cat_name; ?></h3></a>

 <?php endforeach; ?>
</div>
 <?php
} 
// register shortcode
add_shortcode('showcategories', 'my_categories_shortcode');

What should i add, to exclude categories?

Thanks in advance!

EDIT

Thanks, i solved this by adding a continue function as mentioned by Tom Nowell. I have also added the hint that this is a string to the function:

// Function to create shortcode of all categories
function my_categories_shortcode() : string { 
 
// extracting categories
$args=array(
  'orderby' => 'name',
  'order' => 'ASC',
)

?><div class="categorylist">
 <?php foreach (get_categories( $args ) as $cat ) : 
    if ($cat->term_id == 19) {
        continue;
    }
 ?>

<a class="categorylink" href="<?php echo get_category_link($cat->term_id); ?>"><img src="<?php echo z_taxonomy_image_url($cat->term_id); ?>" />
<h3 class="categoryname"><?php echo $cat->cat_name; ?></h3></a>

 <?php endforeach; ?>
</div>
 <?php
} 
// register shortcode
add_shortcode('showcategories', 'my_categories_shortcode');

Answer 1

The solution is already in your code:

 <?php foreach (get_categories( $args ) as $cat ) : ?>

<a class="categorylink" href="<?php echo get_category_link($cat->term_id); ?>"><img src="<?php echo z_taxonomy_image_url($cat->term_id); ?>" />

More specifically:

 <?php foreach (get_categories( $args ) as $cat ) : ?>

...get_category_link($cat->term_id)...

That term_id is the ID of the category, so just test if it matches one of your undesired IDs and continue; to skip to the next one.

---

However, there is an unrelated but super critical mistake in your code. Shortcodes do not echo/output directly. They need to return their output in a string. This shortcode will break a lot of things, and will appear in the wrong place.

Remember:

function brokenshortcode() {
    ?><p>I am an awful shortcode that breaks lots of things</p><?php
}
add_shortcode( 'broken', 'brokenshortcode' );

function niceshortcode() : string {
    return '<p>I am a good well behaved shortcode</p>';
}
add_shortcode( 'nice', 'niceshortcode' );

You can enforce this by type hinting the function like this:

function my_categories_shortcode() : string {

Now the function will cause a PHP fatal if you make this mistake