Do cats claws grow back??

recently my old cat got into a fight and broke a claw! most of the time the claw is fine but then every now and then it bleeds - mainly when he decides to chew at it. the paw isnt swollen and the claw doesnt have any infection. i have been regulary cleaning it and he does let me touch the claw so he isnt in any... show more recently my old cat got into a fight and broke a claw! most of the time the claw is fine but then every now and then it bleeds - mainly when he decides to chew at it. the paw isnt swollen and the claw doesnt have any infection. i have been regulary cleaning it and he does let me touch the claw so he isnt in any pain! just wondering does the claw grow back????
Update: he isnt limping thank god but he has decided that he now likes to have cuddles - think he may be feeling sorry for himself
Update 2: and he has been fixed!!! lol
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