We are currently busy in calculus in proving limits of series ans sequences exist and so on. We use epsilon arguments to prove these things. Somewhere in the proof, the Archimedian Property is used i.e. for every real number x there exists a natural number k such that k > x. I dont understand why this is needed. Can someone please shed some light on this for me? Help me to underdtand this method of proving things. It doenst seem at all logical to me.