#Pushforward

[jaggedjawjosh]

In every step she takes, leadership blossoms, lovingly guiding others to find courage and hope amidst life's challenges.

[harperdo0d1e]

Day 1 - Post-Examination

Survived.

Scared that I might've failed Filipino cause Test I was so hard, I didn't really study on that one 😭

English and CLE were a breeze. CAN wait for tmr, I already need a break lmao.

🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻🌻

[teampropertiesgroup]

Good things are ahead with the new year 🙌 Keep going!

[fhealync]

🌱 Keep pushing forward, and you'll find growth in every challenge. 💪 . . . #KeepGoing #KeepGrowing #MotivationMonday #GrowthMindset #PushForward #NeverStopGrowing #JourneyOnward #LifeJourney #PersonalGrowth #ChaseYourDreams #DailyInspiration #MindsetMatters #SelfImprovement #StayMotivated #GrowthJourney #ProgressNotPerfection #EveryStepCounts #ElevateYourself #RiseAndGrind #ChallengeAccepted #BelieveInYourself #PathToSuccess #EvolvingEveryday #GrowthGoals��#fhealync

[judiawoods]

Keep Swimming

During a study at Harvard in the 1950s, Dr. Curt Richter placed rats in a pool of water to test how long they could tread water. On average they’d give up and sink after 15 minutes. But right before they gave up due to exhaustion, the researchers would pluck them out, dry them off, let them rest for a few minutes – and put them back in for a second round. In this second try – how long do you…

[joelekm]

Push Forward Through Every Challenge | short motivation for athletes

"Push Forward Through Every Challenge" - A short burst of motivation specially crafted for athletes! 🏋️‍♂️🏃‍♀️ Join us in this power-packed video to ignite your inner champion and conquer obstacles on your athletic journey. Get ready to break through limits and achieve greatness.

[positively-knotted]

Because people seem to disagree with me:

[blackpugskateboards]

Skating isn’t just a sport—it’s a statement.

Every push forward is proof that you don’t need to fit in when you were born to stand out.

This is your permission slip to chase joy, fall loud, and get back up with flair.

If you’re a beginner, a comeback kid, or just skating through life—welcome to the rebellion on wheels.

Let’s build a crew that backs each other and keeps it rolling.

Drop a comment if you’re learning, dreaming, or just vibing with this energy—let’s ride together.

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#FallenAngelSkateCo #SkaterGirlVibes #BeginnerSkater #SkateLife #SkateRebel #SkateAustralia #WomensSkateboarding #LearnToSkate #MillennialSkater #SkaterCommunity #SkateInspo #SkateAndCreate #SkateFam #PushForward

[motivationshala]

View this post on Instagram

A post shared by MotivationShala (@motivationshala09)

“🌟 Don’t just dream it, start now! Each step you take brings you closer to your goal. 🌱 What’s holding you back? Break free, take action, and make progress every single day! 🔥 Let’s make this journey together! 💬 Share your story below.👇” #StartNow #MakeProgress #DailyGrowth #SuccessJourney #SelfImprovement #DreamBig #MotivationDaily #PushForward #KeepGoing #GoalSetting #ActionTakers #MotivationShala

[digiavenir]

🌟 Don't Quit, Keep Going! 🌟

At Digiavenir, we understand that the journey of achieving your digital goals can be challenging.

Visit Us: www.digiavenir.com Email : digiavenir@gmail.com

#digiavenir #digitalmarketing #dontquit #digitalsuccess #keepgoing #webdesign #appdevelopment #seo #keepgoing #staystrong #persevere #pushforward #dontstop #youcandoit #believeinyourself #dontquitnow #dontgiveup

[tensorboi]

ok i actually have an answer here omg. my favourite construction is... the functorial description! essentially, to each manifold M you assign a vector bundle TM (which basically bundles up all your tangent spaces into one big space), and to each map f: M -> N you assign a bundle map Tf: TM -> TN which is basically the derivative. here are the technical details (duck if you hate category theory, because you're about to get blasted with it):

There is a functor T from the category of smooth manifolds to smooth vector bundles satisfying the following two properties:

1. On Euclidean spaces: the vector bundle TR^n over R^n is the trivial bundle R^n × R^n, and the output of a map f: R^n -> R^m is the derivative Tf = (f, df): R^n × R^n -> R^m × R^m.

2. Given a manifold M and an open submanifold U, the vector bundle TU is just the restriction of the vector bundle TM to U. Furthermore, if f: M -> N is a map between manifolds and f|U is the restriction of f to U, then the map T(f|U) is just the restriction of Tf to U.

This functor is unique up to natural equivalence. The vector bundle TM is called the tangent bundle of M, and the bundle map Tf is called the pushforward of f (sometimes denoted by df or f_*).

i love this description for so many reasons:

firstly, all of the others slot into this description! for instance equivalence classes of curves make the tangent bundle, and if c is a curve on M and f: M -> N then f ○ c is a curve on N, so Tf([c]) = [f ○ c].

secondly, it demonstrates the generic properties of the tangent bundle so clearly. in the case of euclidean spaces, you really are just sticking a copy of R^n to each point of the space. moreover, locally, the pushforward is literally just the derivative.

thirdly, you immediately get a topology out of it! with all the other descriptions, you have to fiddle a bit to make a topology once you bundle them up. but here it practically falls out: your tangent bundle is locally just TR^n ≈ R^2n, which has a natural topology, and you patch them together via transition functions. it's so clean and elegant!

finally: it's coordinate free, but the coordinates are always there when you need them! not once in the definition do you even mention a coordinate chart, but the entire idea is so readily compatible.

if you want to learn the specifics of this definition, check out spivak vol 1!

[addictedchicago]

[allevallie]

[stuartreardon17]

Life on the edge. . It's only dangerous if my grip fails, mine is stronger than oak, nicknamed gripper from a young age my grip has never let me down. . Disclaimer: Kids, please don't try this at home or your nearest Mountain range, I also have a bulletproof safety backup, I have two large sets of wings tattooed on my ribs and obliques, so if my grip did fail, which it won't, by the laws of gravity by Sir Isaac Newton, in theory, I would gently glide down to the surface unharmed......so technically it's not dangerous at all for me. . workout anywhere and always #pushforward @samuraisportswear . Enjoy your Saturday people. (at Warrington, England) https://www.instagram.com/p/CdQGDVsOfRb/?igshid=NGJjMDIxMWI=

[simplysnipes]

Push Through.

[searchdeepwithinmysoul]

What a tragedy it is... To live in a world where your mind is your worst enemy. To have it destroy you on the inside, yet a smile still merges on the outside. Oh what a tragedy to have a mind like mine. Sleepless night. Constant deep thoughts, worries, fear, pain, & constantly feeling like you're about to lose control. Screaming for help inside your mind begging to let it all out yet trapped inside. So many people are drawn to the love & care you tend to give. To have a heart so big & to love so strong, yet constantly hurt & always alone trapped inside your mind begging to be free, but with heart like yours that'll never be the case you see. To drown in your mind every day but able to grasp a short small breath to keep fighting on. It's a struggle every day, a constant war inside your head. Yet you fight on. Trying your best to not let it shown but the pains so unbearable & so many fear of the unknown. The tears they fall like rain every day & all that's left is a pain that never seems to go away. This is the life I live. This is my life you see. Forever I fight my mental illness even though I know I'll never be free.