As a follow-up to my post listing definitions related to the beginning of human life, here are some diagrams I drew (using my mad skills in Microsoft Paint) illustrating how human fertilization takes place. These raster drawings do not do justice to the miracle of the beginning of a human life, but I hope they clarify the technical aspects.
 | The egg and sperm immediately before fertilization. Each has a haploid nucleus containing one of every chromosome.*
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 | The cell membranes of the egg and sperm fuse. This can be said to be the moment of fertilization. Instead of two gametes, there is now a single zygote.
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 | As the cell membrane fusion is completed, the nuclei remain separate. The cell itself is thus diploid (containing two copies of every chromosome), but instead of one diploid nucleus, it contains two haploid nuclei. The sperm's tail degenerates.
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 | The nuclear membranes (not shown) dissolve and the chromosomes replicate. The result is that the zygote now contains two diploid sets of DNA in preparation for the first cell division (mitosis).
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 | The DNA intermingles into two bodies of chromosomes, each of which comes half from the egg and half from the sperm. These begin to undergo mitosis.
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 | A cell membrane forms across the middle of the zygote, resulting in two cells. It is now an embryo, not a zygote. Each cell contains a diploid nucleus containing a full copy of both the egg's and the sperm's chromosomes.
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*For the sake of simplicity, I omitted the completion of meiosis in the egg's nucleus from these illustrations.