Ethereum is the name of the currency used within the Ethereum network. Ethereum is the crypto-fuel for the decentralized apps on the Ethereum network. Also called crypto asset, it can be used on a peer-to-peer and decentralized computer network, designed to work as a medium of exchange using cryptography to secure the transactions.
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For each electronic wallet there are two addresses: the private and the public address. The private address should never be shared with others, since it gives access to your wallet; the public one is like your traditional bank account number.
More information on Ethereum wallets can be found below: