In order to know what “being Eucharist to others” means, you need to know what “Eucharist” means.
“Eucharist” comes from the Greek “eucharistein”, which means “to give thanks” or “thanksgiving”. The word in Catholic (and Orthodox) circles has also taken on the sense of a sacrifice: to give (by means of sacrifice) thanks. So the Eucharist of the Church is a sacrifice of thanksgiving. It is also the sacramental and real presence of Jesus Christ.
So what does it mean to “be Eucharist” to someone? It can mean:
To carry out Christ’s ministry toward another person, e.g. to be charitable, merciful, etc.
To be self-sacrificing for someone else’s good.
To express, through your interaction with someone else, your thanks to God.
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