Claim Definition - What is a claim?

Claim is a word that you hear again and again, especially in connection with faucets. Claim is an English word and means claim or demand. You "claimed" your coins (Bitcoin, Ethereum, Litecoin etc.) with a Faucet, so you claim it. Most of the time you have to fill in 1 captcha and then you can claim your coins. Unfortunately, many faucets require you to use shortcuts before you can claim.
But this is very time consuming and the payment is often bad, so such faucets are often not profitable and are a waste of time. However, there are exceptions where regular claiming is worthwhile.

Faucets:
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Historical connection to the gold rush, Wikipedia writes about it:

"The concept is based on the Mexican mining law, by which the mining rights belonged to the finder of the mineral resources. The size of a claim corresponded to what could be mined by an individual or a small group. The claim right was introduced in the USA during the California Gold Rush of 1848. From there it spread throughout the Western States. The US Congress legalized the concept in 1866 and implemented it in the Mining Act of 1872, and the right of claim was also applied in other states, for example during the Australian gold rush that began in 1851.

Of course you can't compare the two concepts directly, there are 150 years of history in between, but the word "claim" in crypto currency builds on that.