The relative permeability of a material (\(\mu_r\)) is a measure of how much the material becomes magnetized when exposed to a magnetic field. When the relative permeability is slightly greater than 1, it indicates that the material is weakly attracted to magnetic fields, which is characteristic of paramagnetic materials.
Given the condition that \(1 < \mu_r < 1 + \epsilon\), where \(\epsilon\) is a small positive number, the material is identified as paramagnetic.
Thus, the material is paramagnetic.