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I read in my book that "two alleles are considered to be homozygous if they are identical". But at the same time I read the definition of allele to be:

genes which code for a pair of contrasting traits are called alleles

My doubt is that how can they be both contrasting (different) and identical (same) at the same time

What I think is that if homozygous is somehow a part of specific conditions in alleles then how can it be different from alleles itself.

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These are just issues with singular and plural and whether you refer to individual copies or categories/types.

Two of the same allele copies are the same allele (category/type). Two different alleles (copies) can also be different (categories/types).

In the context of a diploid individual, they have two instances of each gene so therefore two alleles; these alleles can be the same or different.

So you can say you have two "red flower" alleles, meaning two copies of the red flower allele. Or you can have a population that has two alleles for flower color: red flower alleles or white flower alleles.

The same is used in English for other things. You might say a farm grows two fruits, peaches and plums, and also that I have two fruits in my hand, both peaches. You need to use surrounding context to recognize whether copy or type is meant.

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