Help on if-else in shell

What about

#!/bin/sh

i=1
n=2

if [ "$i" -gt "$n" ]; then 
    echo "i is bigger" 
elif [ "$n" -gt "$i" ]; then 
    echo "n is bigger" 
else 
    echo "same" 
fi

second...

#!/bin/bash

i=1
n=2

if ((i > n)) ; then 
    echo "i is bigger" 
elif ((i < n)); then
    echo "n is bigger"
else
    echo "same"
fi

and last one...

#!/bin/bash

i=1
n=2

if [[ $i -gt $n ]]; then 
    echo "i is bigger"
elif [[ $i -lt $n ]];  then
    echo "n is bigger"
else
    echo "same"
fi

I have the following script to make sure some services stay up. It also does a mysql backup everyday, checks for services online and if not they go up again, etc.. Not my best work but gives you an idea on how to use IF and the same goes for ELSE IF:

#!/bin/bash
function checker() {
    PID1=$(pidof authserver)
    PID2=$(pidof worldserver)
    PID3=$(date +%k%M)
    PID4=$(date +%d_%m_%y)
    Destiny=/root/bck
    if [ -z "$PID1" ]; then
    echo 3 > /proc/sys/vm/drop_caches
            screen -A -m -d -S auth ./bin/authserver
    fi

    if [ -z "$PID2" ]; then
    echo 3 > /proc/sys/vm/drop_caches
            screen -A -m -d -t titan -S world ./bin/worldserver
    fi

    if [ "$PID3" -eq 230 ]; then
            screen -S world -p titan -X stuff $'anno SERVIDOR CERRADO DENTRO DE 10 MINUTOS POR UNA DURACION DE 30 SEGUNDOS PARA OPTIMIZACIONES\n'
            sleep 300
            screen -S world -p titan -X stuff $'anno SERVIDOR CERRADO DENTRO DE 5 MINUTOS POR UNA DURACION DE 30 SEGUNDOS PARA OPTIMIZACIONES\n'
            sleep 180
            screen -S world -p titan -X stuff $'anno SERVIDOR CERRADO DENTRO DE 2 MINUTOS POR UNA DURACION DE 30 SEGUNDOS PARA OPTIMIZACIONES\n'
            screen -S world -p titan -X stuff $'ser shut 120\n'
            sleep 120
            /etc/init.d/apache restart
            sleep 5
            mysqldump -uroot -px chart > $Destiny/c$PID4.sql
            mysqldump -uroot -px auth > $Destiny/a$PID4.sql
    /etc/init.d/mysql restart
            sleep 5
            killall -9 worldserver
    killall -9 authserver
    echo 3 > /proc/sys/vm/drop_caches
fi
    return 1
}
while :
do
checker
sleep 5
done

Like I said, not the best but gets the job done.