What does the word one in John 10:30 and Mark 12:29 mean?

Question

Mark 12:29 YLT and Jesus answered him -- 'The first of all the commands is, Hear, O Israel, the Lord is our God, the Lord is one;

John 10:30 YLT I and the Father are one

On which verse does it mean (borrowed from Dottard's answer) a single person, or thing, with focus on quantitative aspect, "one", ... (b) in contrast to the parts of which a whole is made up,?

On which verse does it connote unity, agreement, and united oneness?

Answer 1

According to BDAG, the word εἷς, μία , "one" has at least five basic meanings with several sub-meanings for each; however, for these texts of the OP it gives the following meaning:

a single person, or thing, with focus on quantitative aspect, "one", ... (b) in contrast to the parts of which a whole is made up, eg,

• Matt 19:5 - and said, ‘For this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh’?
• Mark 10:8 - and the two will become one flesh.’ So they are no longer two, but one flesh.
• 1 Cor 6:16 - Or don’t you know that he who unites himself with a prostitute is one with her in body? For it is said, “The two will become one flesh.”
• Rom 12:5 - so in Christ we who are many are one body, and each member belongs to one another.
• Rom 12:12 - The body is a unit, though it is composed of many parts. And although its parts are many, they all form one body. So it is with Christ.
• Rom 12:20 - As it is, there are many parts, but one body.
• Eph 2:15 - by abolishing in His flesh the law of commandments and decrees. He did this to create in Himself one new man out of the two, thus making peace
• Gal 3:28 - There is neither Jew nor Greek, slave nor free, male nor female, for you are all one in Christ Jesus.
• 1 Cor 3:8 - He who plants and he who waters are one in purpose, and each will be rewarded according to his own labor.
• John 10:30 - I and the Father are one.
• John 17:11 - Holy Father, protect them by Your name, the name You gave Me, so that they may be one as We are one.
• John 17:21 - that all of them may be one, as You, Father, are in Me, and I am in You. May they also be in Us, so that the world may believe that You sent Me.
• John 17:23 - I in them and You in Me—that they may be perfectly united, so that the world may know that You sent Me and have loved them just as You have loved Me.
• 1 John 5:8 - the Spirit and the water and the blood--and these are three in one. ["agreement" in most versions.]
• Eph 2:14 - For He Himself is our peace, who has made the two one and has torn down the dividing wall of hostility

Thus, the word has very strong connotations of unity, agreement, and united oneness, depending on the context.

Answer 2

The two words are not the same; one is a masculine, and the other a neutral. In Greek, as in Latin, the former refers to a singular masculine entity, whereas the other denotes either a singular neutral entity, or unity. Since fathers and sons are both males, using the masculine word in the second sentence would have implied that Christ is the Father (in which case the simpler expression I am the Father would have been a more natural choice). If instead of a father and a son we'd have two neutral nouns, or two nouns of distinct genders, the second expression would have been ambiguous. As it stands, however, there is no ambiguity there. Christ is one with the Father, without actually being (the same as) the Father.