Can we really pet a stray cat?

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For the past months a cat sneaks in to our house and always makes a mess in our kitchen,in our living room,in our attic and almost every part of our house..I was even pissed when I stepped on a cat's poop in our bathroom..that cat has been our problem eversince.. Now one day when my girlfriend went to the attic and go look for stuff,she found a kitten in a box under a table and it turns out that the cat have been nursing her baby eversince she got here in our house..my girlfriend then took the kitten,went down and showed what she found to me..then ding-a-ling!!an idea popped into my head..I went again in the attic and grab the cage..what I did is I put the little kitty inside the cage and waited for the mother cat to come and get the kitty..I sent my girlfriend down stairs and I told her to let me do the job..I waited for almost an hour and finally the mother cat showed up and yey!!I caught her.. My girlfriend and I wanted a pet eversince so we decided to keep the cat and her kitty as a pet..but there was another problem we have to face..the mother cat and the kitten turned out to be a little bit wild..we always have to sneak into the cage and run whenever we bring them food.. I don't want the cat and the kitten to die of hunger..Me and my girlfriend tries to do the best we can to pet the cats..but everything we do doesn't seem to work.. Please I need help here..thank you to those who will reply..