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When you worship Allah: الله أكبر: Allah is worthy of far more veneration than I can possible give him.
When you see a victory: الله أكبر: Allah's might is infinitely more mighty than this victory.
And so forth. By saying the takbīr, Allah is glorified, unconditionally, in all aspects, against any other being.
الله أكبر الله أكبر ولله الحمد الله