How to turn of internet on iphone 5?

I can use both Wi-Fi and have my own internet. I only want to use Wi-Fi because using internet costs a lot of money. I found out that I was still using the the internet when I turned Wi-Fi off. How do you turn it off?

Settings
General
Cellular Data
- toggle the Cellular Data option to Off. That turns off cellular data, not the phone and/or text abilities.

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