Are ratios with zero defined?

ratio

Are ratios like $4:0$ or $0:4:0$ defined? I saw such ratios being used to describe the phenotype ratio in a mono-hybrid cross – tall plants:short plants $=0:4$.

They are indeed well-defined, so long as at least one number is non-zero. For the given example, it just means no tall plants were observed in the cross.

The ratio colons are sometimes used to denote homogenous coordinates, where another ratio representing some point can be obtained by multiplying all numbers in that ratio by the same number. The origin (all numbers zero) is excluded, and does not represent any point.

Yes, as long as not all coordinates are zero.

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