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But that’s not more that two sexes. It’s the same number or less. A hermaphrodite isn’t a third sex, it’s two sexes side by side and a sexless cellular organism has exactly one sex.
The distinction male/female is usually determined by measuring the size of the gametes. Female gametes are the bigger ones (e. g. ovum) and male gametes are the smaller ones (e. g. spermatozoon). There are organisms where the gametes of both sexes have the same size. So technically they have two sexes but don’t fit the categories male and female.
But wouldn’t the asexual reproducing animal that is one sex be neither male or female and thus is a third?
Sex in the sense that we have been talking about it here is in reference to mammals. The moment you wander outside of the mammalian class of vertebrates these concepts of sex start to become far less applicable.
There are many birds that have more than 2 sexes. Reptiles and invertebrates as well. Asexual reproduction would be classed as it’s own sex apart from any male/female system.
you’re a mammal though right