If I have a dollar and decide to split it between three separate persons as close to evenly as I can then two persons would have ¢33 or % each, and one would have ¢34 or % of the whole dollar.
Individually each would have about a third of the whole. Yet together they would make up the entire whole.
The same simple logic applies to anything that is comprised of three equal parts.
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Your dollar bill analogy doesn't work, or at least your attempt to make it work doesn't.
God is triune. Three in one.
The three Persons coexist as one God.
If my dollar bill were to accurately represent God, I would have a single dollar bill when looking at it from one direction, and three dollar bills, from another direction, yet I would still have only one $1 bill. From the second perspective, each of the three apparent dollar bills would look and feel and smell and sound and taste exactly like the single dollar bill from the first perspective, but they would each be distinct from each other, and from that second perspective, I would have three individual dollar bills. But going back to the first perspective, I would only have one dollar bill.
The above analogy better fits the God of the Bible, and therefore the trinity.