Magic Rub
First Post
Let me re-cap & dissect 
That's right it says "is limited to a certain number of spells of each spell level per day".
Need more proof? Here you go...
Yes that's right it says "a good night’s sleep", & I know or an "equivalent". Regardless this type of rest can only happen once per day as MThibaut's post has already explained.
This "flavour" text, if yo would like to think about it that way, Explains quite clearly how the "spells per day" system is suppose to work. Use all your spells, suffer for the rest of the day without if you used them all, sleep for the night, get up the next morning after a night of rest study & do it all again. not use all your spells, rest for 8 hours, restudy, use all your spells, rest for 8 hours, restudy, use all your spells... ect. ect.
Holy! Would you look at that... "A wizard’s level limits the number of spells she can prepare and cast" probably per the "Spells per day" list.
"A wizard’s high Intelligence score (see Table 1–1: Ability Modifiers and Bonus Spells, page 8) might allow her to prepare a few extra spells. She can prepare the same spell more than once, but each preparation counts as one spell toward her daily limit." This would mean that there is a sum total maximum number of spells you can have per day... Period. Not to be confused with what some people think would be "maximum spell per ever 8 - 9 ish hours".
"The character does not have to slumber for every minute of the time, but she must refrain from... mental task during the rest period"
MThibaut's post sums this up nicely "I deliberately worded my example to show that just because you are lying in bed does not mean that you are resting. Try it. No books, no headphones, and not in the least bit tired? You will be restlessly bored for over half the time you are lying down."
I've always thought that in the case of elven mages, they simply extend their trance / meditation. to a full 8 hours.
"After resting, a wizard must study her spellbook to prepare any spells that day. If the character wants to prepare all her spells, the process takes 1 hour. Preparing some smaller portion of her daily capacity..." I would think this would imply that their is a fixed daily limit as per the "Spells per day" chart.
"had prepared from the previous day" Doesn't this imply that you can only prepare spells once per day to the maximum of your alloted spells as per the spells per day list?
If you can leave slots open? Why would you do that if you could restudy all your spells more then once in a day? Because you can't drop & restudy all your spells that's why... "She cannot, however, abandon a previously prepared spell to replace it with another one or fill a slot that is empty because she has cast a spell in the meantime.That sort of preparation requires a mind fresh from rest." a mind fresh from rest... have you ever slept to much or sat around, resting or sleeping, for 8 hours after having had a full nights sleep. You do not feel FRESH in mind, or body. You feel ill, generally with a head ache, groggy & slow.
Sorry if I came across sarcastically in this post, it was unintentional. I just think that it is abundantly clear that Wizards (as with all spell casters) do indeed have a maximum number of spells per day cap as listed in the chart in the wizards class section of the PHB (modified by the bonus spells per day list of course)

From the wizard class description - under Spells:
...A wizard casts arcane spells. She is limited to a certain number of spells of each spell level per day, according to her class level.
That's right it says "is limited to a certain number of spells of each spell level per day".
Need more proof? Here you go...
From the wizard class description - under Spells:
...A wizard must prepare spells ahead of time by getting a good night’s sleep and spending 1 hour studying her spellbook...
Yes that's right it says "a good night’s sleep", & I know or an "equivalent". Regardless this type of rest can only happen once per day as MThibaut's post has already explained.
FROM PREPARING WIZARD SPELLS:
Before setting out on an adventure with her companions, Mialee (at 1st level) pores over her spellbook and prepares two 1st-level spells (one for being a 1st-level wizard and an additional one as her 1st-level bonus spell for Intelligence 15) and three 0-level spells. (Arcane spellcasters often call their 0-level spells "cantrips.") From the spells in her spellbook, she chooses charm person, sleep, detect magic (twice), and light. While traveling, she and her party are attacked
by gnoll raiders, and she casts her sleep spell. After she and her companions have dispatched the gnolls, she casts detect magic to see whether any of the gnolls’ items are enchanted. (They’re not.) The party then camps for the night in the wilderness. Come morning, Mialee can once again prepare spells from her spellbook.
This "flavour" text, if yo would like to think about it that way, Explains quite clearly how the "spells per day" system is suppose to work. Use all your spells, suffer for the rest of the day without if you used them all, sleep for the night, get up the next morning after a night of rest study & do it all again. not use all your spells, rest for 8 hours, restudy, use all your spells, rest for 8 hours, restudy, use all your spells... ect. ect.
...further FROM PREPARING WIZARD SPELLS:
She already has charm person, detect magic (once), and light prepared from the day before. She chooses to abandon her light spell and then prepare sleep, detect magic, and ghost sound. It takes her a little over half an hour to prepare these spells because they represent a little over half of her daily capacity. A wizard’s level limits the number of spells she can prepare and cast (see Table 3–20: The Wizard, page 52). A wizard’s high Intelligence score (see Table 1–1: Ability Modifiers and Bonus Spells, page 8) might allow her to prepare a few extra spells. She can prepare the same spell more than once, but each preparation counts as one spell toward her daily limit. Preparing arcane spells is an arduous mental task. To do so, the wizard must have an Intelligence score of at least 10 plus the spell’s level.
Holy! Would you look at that... "A wizard’s level limits the number of spells she can prepare and cast" probably per the "Spells per day" list.

"A wizard’s high Intelligence score (see Table 1–1: Ability Modifiers and Bonus Spells, page 8) might allow her to prepare a few extra spells. She can prepare the same spell more than once, but each preparation counts as one spell toward her daily limit." This would mean that there is a sum total maximum number of spells you can have per day... Period. Not to be confused with what some people think would be "maximum spell per ever 8 - 9 ish hours".
Rest:
To prepare her daily spells, a wizard must have a clear mind. To clear her mind, the wizard must first sleep for 8 hours. The character does not have to slumber for every minute of the time, but she must refrain from movement, combat, spellcasting, skill use, conversation, or any other fairly demanding physical or mental task during the rest period.
"The character does not have to slumber for every minute of the time, but she must refrain from... mental task during the rest period"
MThibaut's post sums this up nicely "I deliberately worded my example to show that just because you are lying in bed does not mean that you are resting. Try it. No books, no headphones, and not in the least bit tired? You will be restlessly bored for over half the time you are lying down."
...further from Rest:
If the wizard’s rest is interrupted, each interruption adds 1 hour to the total amount of time she has to rest in order to clear her mind, and the wizard must have at least 1 hour of rest immediately prior to preparing her spells. If the character does not need to sleep for some reason, she still must have 8 hours of restful calm before preparing any spells. For example, elven wizards need 8 hours of rest to clear their minds even though they need only 4 hours of trance to refresh their bodies (so they could trance for 4 hours and rest for 4 hours and then prepare spells).
I've always thought that in the case of elven mages, they simply extend their trance / meditation. to a full 8 hours.
from Spell Preparation Time:
After resting, a wizard must study her spellbook to prepare any spells that day. If the character wants to prepare all her spells, the process takes 1 hour. Preparing some smaller portion of her daily capacity takes a proportionally smaller amount of time, but always at least 15 minutes, the minimum time required to achieve the proper mental state.
"After resting, a wizard must study her spellbook to prepare any spells that day. If the character wants to prepare all her spells, the process takes 1 hour. Preparing some smaller portion of her daily capacity..." I would think this would imply that their is a fixed daily limit as per the "Spells per day" chart.
from Spell Selection and Preparation:
Until she prepares spells from her spellbook, the only spells a wizard has available to cast are the ones that she already had prepared from the previous day and has not yet used..
"had prepared from the previous day" Doesn't this imply that you can only prepare spells once per day to the maximum of your alloted spells as per the spells per day list?

further from Spell Selection and Preparation:
...When preparing spells for the day, the wizard can leave some spell slots open. Later during that day, the wizard can repeat the preparation process as often as she likes, time and circumstances permitting. During these extra sessions of preparation, a wizard can fill these unused spell slots. She cannot, however, abandon a previously prepared spell to replace it with another one or fill a slot that is empty because she has cast a spell in the meantime. That sort of preparation requires a mind fresh from rest. Like the first session of the day, this preparation takes at least 15 minutes, and it takes longer if the wizard prepares more than one-quarter of her spells.
If you can leave slots open? Why would you do that if you could restudy all your spells more then once in a day? Because you can't drop & restudy all your spells that's why... "She cannot, however, abandon a previously prepared spell to replace it with another one or fill a slot that is empty because she has cast a spell in the meantime.That sort of preparation requires a mind fresh from rest." a mind fresh from rest... have you ever slept to much or sat around, resting or sleeping, for 8 hours after having had a full nights sleep. You do not feel FRESH in mind, or body. You feel ill, generally with a head ache, groggy & slow.
Sorry if I came across sarcastically in this post, it was unintentional. I just think that it is abundantly clear that Wizards (as with all spell casters) do indeed have a maximum number of spells per day cap as listed in the chart in the wizards class section of the PHB (modified by the bonus spells per day list of course)
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