I am an 8-letter word. I have a special property that can be a headache for many scholars. Every day, I lose a letter and subsequently rearrange myself into a meaningful word.

Based on the hints provided below, guess the word on Day 0.

1. On Day 1, I am what dreamers do.
2. On Day 2, No one can understand me.
3. On Day 3, I finally get imprinted in everyone's memory.
4. On Day 4, Everyone loves me, or at least some types of me.
5. On Day 5, I realise I can only ever increase, and cannot be fought.