Note that most useful homomorphic numerical encryption schemes are easily breakable. Once you have equality you can usually de-anonymize user data. Many companies have been burnt by this.

With a less than operator and the ability to encrypt chosen plaintext values, you can decrypt arbitrary messages in a linear (in message size) number of steps.

Arithmetic operations can often be used to build gadgets that bootstrap comparison operations. For instance, with addition and equality you can implement a comparison operation for low-medium cardinality fields.

The field is littered with negative results that are being sold as secure, practical systems. Be careful when using them on important data.