How to check if a user exists by a given id

Use this function:

function user_id_exists($user){

    global $wpdb;

    $count = $wpdb->get_var($wpdb->prepare("SELECT COUNT(*) FROM $wpdb->users WHERE ID = %d", $user));

    if($count == 1){ return true; }else{ return false; }

}

Usage:

if(user_id_exists(1)){ 
    //it does exists
} else {
    //it doesn't
}