Many of us have heard this question asked "Can God make a rock so big He can't lift it?"
Here's the answer...
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Omnipotent does not imply "capable of anything". Being all powerful does not mean being without constraints of character. God is not able to do contradictory things because He is rational. It is not philosophically sound to set up a false version of omnipotence and then try and disprove it with an irrational idea. Omnipotence is a theological term, so the best sources for an understanding of it are theological dictionaries and works.
here are excerpts about "Omnipotence" from theological works
"Divine power is only limited by the absurd and self-contradictory...
God can not do anything inconsistent with the divine nature."
"Dogmatic Theology" by Shedd, Third Edition pg 289
"God is all powerful and able to do whatever He wills. Since His will is limited by His nature, God can do everything that is in harmony with His perfections"
"The Moody Handbook of Theology" pg 195