What Is the Genetic Code?

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Tyto alba
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According to https://www.ncbi.nlm.nih.gov/books/NBK21950/ and some other sources:

'Genetic code is the set of correspondences between nucleotide pair triplets in DNA and amino acids in protein.'

What dose correspondences mean in this regard?
I don't understand why nucleotide pair triplets and not simply nucleotide triplets?

P.S. I'm aware of codon and translation.
 
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Pairs simply because they are naturally stored as pairs (double-strand). A single strand is sufficient to have all the information, but it is less stable, and you need the pairing mechanism to copy it.
 
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And what dose correspondences mean in this regard?
 
Every triplet encodes a single amino acid. The sequence UGU "corresponds" to Cysteine, for example: If the DNA has this triplet, and it is translated, the cell will add Cysteine. UGC also corresponds to Cysteine. Here is a full diagram, to be read from the inside outwards.
 
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@mfb very good chart, wish I had one like it for teaching years ago.

But. DNA has thymine, not uracil. Uracil is the thymine 'analog' in RNA. So the nice chart is based on the triplets in RNA.
 
Ah, didn't think of the conversion. The chart is for RNA as the RNA is translated to amino acids. The DNA is translated to RNA before, with T->U.