I am not sure that this is mathematics but nether the less I will still answer. Bad people exist because of many things. For one, the human itself is selfish and greedy ( not all humans are). We want power, which is some causes of war, and money and everything are never enough. Sometimes bad people are put in your life to help you. Even though it does not seem like it, they are your obstacles in life. They are put there for you to help or other things. One thing is that if a person is a bully to you, overcoming that bully and going on with life shows how strong you are and pushes you around an obstacle. The other big obstacle in this scenario is that you could try and help the bully. That would be a big challenge since they hurt you but they could also be hurting. That doesn't mean what they are doing is an excuse or anything, it could just mean they are going through something and may not know how to handle it so they take it out on others. In the end, most bullies actually feel bad for what they did. Trying to be their friend is something that, even with lots of hard work and patience, has amazing results. I know from personal experience. Though this is just an example, bad people most of the time are hurting good people who just need care. The bad people are there so we can overcome the things they throw at us and then we can help them. Sometimes some people are very hard to help but that doesn't mean we shouldn't try. Sociopaths are people that seem to be beyond helping but even so you can try and help them even when it may not seem right. Putting them in jail for a crime seems like a bad choice but saving more people is what is taught to be better. If you tried to help a person who seems to be beyond help than you can help them by giving them counseling, leaving them be, or even just saying hello and how are you doing every day. Don't look at bad people and see hate or evil but rather a lost person who needs guidance. Sometimes it will be hard since there are really bad people out there who could really hurt you but that shouldn't dim a spark of light.
