19.6 por + adjective / adverbe + que + subordinate clause = no matter how + adjective / adverb + subordinate clause
This conjunction is a variation of ainda que, mesmo que etc.. The difference is that the event in the main clause is going to happen irrespective of the intensity of the event described in the subordinate clause.
| No matter how small he is, he will not be able to pass through. |
| No matter how ill they are, they go to the beach. |
| No matter how fast he runs, he will never be as fast as he. |
Given that the quantitative / qualitative intensity is unknown, these kind of constructions requires the conjuntivo.
| por + Adjektiv / Adverb + que + Nebensatz = so / egal wie + Adjektiv / Adverb..... que Nebensatz |
E por mais que eu deteste admitir, acidentes acontecem.  |
| No matter how hard it is for me to admit it, accidents occur. |
| Por muito inteligente que ela seja, ninguém pode mudar o passado. |
| No matter how intelligent she is, nobody can put the clock back. |
| Não consegues parti-las, por muito forte que sejas. |
| No matter how strong you are, you won't be able to break it. |
| Por maior que o tipo fosse, eu não desistia. |
| No matter how strong the chap is, I never would recoil. |
| Subordinaram a sua ajuda a alguma condição, por menor que fosse? |
| Did they subject the help to a condition as little it may be? |
This construction shouldn't be confused with mais / menos que. This is a simple comparative with the preposition por.
| mais / menos que comparative |
| O cérebro pode viver sem oxigénio por mais que um minuto. |
| The brain can live more than one minute without oxygen. |
| Eles tentaram apanhar-me por mais que uma vez. |
| They tried more than one time to catch me. |
| Já matou gente por menos que isso. |
| He already killed people for less than that. |
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